WARNING: This gets pretty spoiler-y as the theory I am presenting today looks heavily at major plot scenes and endgame content. If you are trying to avoid spoilers for the game, please scroll away now.

Sayori. Oooh, Sayori....
This girl is living (or non-living) proof that looks can be deceiving. Perhaps all the girls fit this description, but Sayori most of all, for a number of reasons. One of these reasons is something we're all familiar with, but the main one is something that I find a lot of people simply skim over. To put it briefly, the revelation of this goes like "Thanks for deleting Monika! Now I'M the president, and I can do whatever I want! You're going to be with me...FOREVER!"

...Yup. Sayori had simply been deceiving you the whole time.
Okay, so her little reveal wasn't THAT over-the-top and evil-sounding, but the point stands that all along Sayori had just been manipulating you in order to become president of the literature club. In order for that to happen, Sayori needed Monika dead - we know this because after the player deletes Monika in Act 3, Sayori inherits her role as president. But what for? What exactly was Sayori planning to do with this power? More to the point, why did Monika feel the need to come back and stop her?
Let's look at the facts....

Sayori's plan - Act 1
(Had to improvise with the headings - gosh darn, I miss the old forums)

We've already established who Sayori is - she's the vice-president of the club and is looking to claim the top spot. But in order to fully understand her, we must first take a look at how this evil scheme plays out. And since DDLC is a long game with a lot of dialogue, you'd best be ready to read lots - we're gonna be here for a while.

In Act 1, Sayori is the first character we meet. She persuades the protagonist to join the titular club and is known for the "atmosphere" her presence brings to the club - your average 'ray of sunshine' character archetype. However, it soon becomes apparent that all is not as it seems. On Friday, Sayori leaves the club early, and her absence notably disrupts the atmosphere. The other girls become disturbed, and even start to turn on Monika a little, but as we all know this is only the start. The weekend rolls around and Sayori reveals her happy-go-lucky attitude was simply a mask for a serious case of depression. But hold on a second - how does this relate to Sayori being an evil mastermind?
The answer is pretty simple. As she said before, she acted happy to try and hide her true feelings. It's a metaphorical mask, and a mask can hide almost anything. So if it can hide depression, it can hide villainy too.

But knowing this raises even more questions, specifically regarding one of the most infamous scenes in the game - why did Sayori kill herself? In order to answer this, we need to take a step back and establish what Sayori's goals mean for her. Being the club president, Monika is in a position of authority, for sure, but there's a little more to it than that. Throughout the game, Monika demonstrates her ability to control aspects of the game, manipulating the other girls' dialogue (you'll know it's her because the outline is noticeably thicker on modified lines) and the game code to change it to suit her liking. So if you're president, you control the game. Cool, right? And we know that the power comes from being the president because in the twist ending, Sayori is able to use the 'glitch' effects that Monika uses, changing the background to fit her speech. How could she pass this up?

With that in mind, let's turn our attention back to Sayori's death scene. You'll notice that when the camera zooms in on her face, static appears on the screen and an error message appears in the background. More to the point, a file called "traceback.txt" is written to the game folder - "traceback" being a term used by Python to refer to errors in a program's code. Sayori's death had caused something to go wrong, and this becomes even more apparent when reading the newly-written file. A section called "RestartTopContext" is located near the top and bottom of the document, which contains the following message:

"Oh jeez...I didn't break anything, did I? Hold on a sec, I can probably fix this...I think...
Actually, you know what? This would probably be a lot easier if I just deleted her. She's the one who's making this so difficult. Ahaha! Well, here goes nothing."

I would like to draw your attention to that last bit in particular - "She's the one who's making this so difficult." It's because of Sayori herself that this error occurs. And since Monika controls the game as president, it would be her job to look out for stuff like this - after all, what use is having complete control over a program if it doesn't work?
Therefore, it can be safely concluded that this was not an actual suicide attempt, but an attack. An attack on the game which Monika controls. Sayori chose to hang herself because most visual novels don't deal with that stuff, and since DDLC is (in a story sense anyway) a romance-based game, it wouldn't be able to handle Sayori's suicide. And if Monika can't fix it, then she has no choice but to give up, which would allow Sayori to inherit the role.
But Monika was smarter than Sayori had anticipated. The RestartTopContext states that Monika had to "delete her", which we know effectively means deleting the .chr file in the 'characters' folder to 'kill' them (it's part of a coding illusion where the actual game is concerned).

And what happens after that? sayori.chr is removed from the game!

So suicide didn't work. On to phase 2....

Sayori's improvisation - Act 2
Now here you all are scratching your heads. "Sayori's dead, isn't she?" I hear you ask. And to answer that question, yes and no. Sayori was deleted, sure, and her body is now positively dead, but that doesn't mean she's well and truly finished. To understand what happens after someone is deleted, we need to take a look at Monika and how her deletion plays out. When you delete her file, her sprites are removed from the game - she can't physically appear to you. However, as evidenced by the ending scene, Monika was still able to exploit the game's code as a means of persisting after death, with just enough power to stop Sayori. Keep in mind that at this point Monika was not the president in total control - Sayori was. This shows us that persisting after death is not a president power - anyone can do it. So if Monika could do it at that point, so can Sayori.

But now we have the question of what she actually did in those moments. What did Sayori do that was so integral to this scheme?
Well, there are two other girls you can date, aren't there? The focus shifts to Yuri and Natsuki in Act 2.

Firstly, let's see if we can link them both to Sayori. All three of these girls are 'dateable' - they have their own routes. Another thing to note is that they all wear the same clothes - white knee-high socks with blue shoes. Meanwhile, Monika is cast out as an anomaly because she wears black thigh-highs and pink shoes and doesn't have her own route.
So something, somewhere, is tying the other three together...

...Of course! Yuri and Natsuki are Sayori's goons! That's why they are so thrown off when their mistress leaves them, and also why they antagonized Monika so much, trying their hardest to stop her from getting what she wants. It's through these two girls that Sayori was able to continue her work posthumously. So let's analyse their roles in this plot and how it all plays out.

Natsuki is arguably the less important of the two, but still plays a part in this plan. When Yuri goes into her 'yandere' phase, Natsuki writes a poem which isn't so much a poem as it is a letter addressing her concern for Yuri. We know that Monika messes with the girls' personalities in a process she calls "untying the knot" - tapping into their negative traits and amplifying them in an attempt to make them look bad. In Natsuki's letter, she seems to be aware of this, mentioning that Yuri has been acting strangely and suggesting that you talk to her in order to calm her down. And given that Monika is quick to act on this, using Natsuki's dialogue to convince you to "ignore everything you just read", it can be safely assumed that this is part of Sayori's plan - she's calling her out to make you hate her enough to delete her.

This can also be seen in Yuri's actions. In one particularly infamous dialogue exchange, Yuri starts trying to make Monika look bad, insulting her and telling her to kill herself. Here, the force of Sayori is giving Monika a taste of her own medicine - after all, she's only been doing the same thing to Yuri for almost the entirety of Act 2, right?
However, Yuri's connection with Sayori can be taken a little further than that. Going back to Sayori's "death" scene, you can see what appears to be a glitched-up version of the main menu, with Yuri of all people being the solitary character glitching about all over the place. Furthermore, when starting Act 2 for the first time, you are greeted with a messed-up version of Act 1's intro, with Sayori being replaced by a glitchy mess of sprites - for the sake of making this easier to read and write, let's call it Broki. What's interesting to note about Broki's sprites is that only two existing characters are seen in them - Monika and Yuri - seemingly in a struggle over who gets to be the most dominant in this display. It's also slightly symbolic of the battle between Monika and Sayori, right?
I think you can see where I'm going with this. In Act 2, Sayori's main method of acting in the game world is through the use of Yuri as a vessel. After death, she passed on to Yuri's body (I'm not sure how) so she could still physically appear and act in the game world, which gave her more options in what to do.

And Yuri's situation sorta mirror's Sayori's as well. Not only does she inherit the role of vice-president after Sayori's death, but at the end of Act 2 she is involved with her own suicide scene, which we know now is Sayori's method of attacking the game. However, Sayori was more careful this time. She knew the last attempt didn't work because the code was damaged to the point where a traceback file was created and Monika was easily able to counter as a result. So instead, Sayori made Yuri's attack more subtle. When Yuri kills herself, you're stuck on a single screen, with garbled text that repeats itself forever. The game is fine in terms of the code, but has effectively grinded to a halt. Only through repeated loading of your save file are you able to get past this sequence and progress with the story. But the attack hasn't finished yet!
In light of this, Monika deletes yuri.chr and natsuki.chr under the impression that they have ruined it for her and the player. But in doing so, she unwittingly falls right into Sayori's trap. We actually see her in the act, unlike last time where Monika could keep the drama relatively hidden from the unsuspecting player.
Monika exposed herself!

And in thinking she's totally safe, Monika changes the game into Act 3, where she reveals what she had been doing to the other girls in order to get her way. Little does she know she's actually painted herself as the villain, which prompts the player (which by the way Monika fans, you HAVE to do in order to progress) to delete monika.chr from the 'characters' folder, ending her reign as president once and for all.

It seems everything has fallen into place after all. Feeling remorse for what she did, Monika uses the last of her president power to restart the game in Act 4, but with her effectively removed from the game (as of course, she's been deleted). This allows Sayori to swoop in and claim the prize she's been chasing after the whole time. At last! Total control and limitless power! Everything went according to plan. Nothing can go wrong now!

Erm, not quite. There is one last fatal oversight that Sayori made - if she could persist after death without being the president, then so could Monika. In a last act of heroism, Monika attacks the game herself, stopping Sayori from rewriting the code again, and shutting it down with a final song and note to the player.
After all, if Sayori can do it, so can Monika.

Sayori's hatred - Finding the motive
So now we know how Sayori goes about her scheme, it's time to answer the big question on everyone's mind - why?
It's finally time to delve into the mind of Sayori....

We know Sayori suffers from depression, and if her speech in Act 1 is anything to go by she's been dealing with it for a long time. This also means it was lingering in Sayori's mind before the protagonist joined the club, as she is late in getting out of bed when Act 1 starts - a trait which is later revealed to be down to depression. And more to the point, Sayori's depression has been there since she first joined the club and met Monika - after all, she had to be around there for quite some time to be able to introduce everyone by their names and most notable personality traits.

So Sayori's been depressed from the start. What does this prove? Well, I'll tell you. It proves that depression could well be the driving force behind Sayori's motives.
Sayori's depressive thoughts are built on the idea that "the world is punishing [her] for being selfish." She believes that because she is selfish, the world punished her by giving her all these sad and depressive thoughts and feelings, which makes it hard for her to cope with life. It's all down to selfishness, she says.

But who else has been shown to be selfish throughout the course of the game? That's right: Monika! Sayori had obviously known Monika for a while - they are seen chatting in the clubroom, seemingly being friends. To have planned this whole uprising against Monika, Sayori had to at some point learned what she was up to - what being president of the club means and how she intended to use that power to steal the player for herself. That scheme sounds selfish, sure, but the world doesn't seem to be punishing Monika for it, does it? Sayori would've definitely felt a sense of injustice because of this - it's almost as if fate has double-standards. Since Monika had this whole scheme of hers from the beginning - even in Act 1 she drops little tidbits about her lore in her poems - it was only natural for Sayori to try and stop her.
Besides, why should her childhood friend go to a woman they barely laid eyes on and considered to be "out of [their] league"?

But that just makes the ending of DDLC a little more confusing. When Monika launches her attack on the game, one of the first things she says to Sayori is "I won't let you hurt him."
Excuse me, what? Hurt you? The player? Why on Earth would Sayori do that? So I tried looking into it a little further, bearing in mind some of the common tropes of DDLC, and here's what I deduced.

We know DDLC to be pretty meta - there's a lot of fourth-wall breakage and it plays out like a twisted version of a standard romance-based visual novel. In most games in this genre, the player is given the ability to save their progress and load the save files they've created. Essentially, you're able to bend the rules of time in these stories, manipulating the progression - and therefore the characters - to get the outcome you want. If you tried doing this in real life, 1: that's physically impossible, but 2: that wouldn't be a very nice thing to do to people. If you manipulate people's memories like that just to get with the one you want, you'd be considered a sociopath in today's society. In fact, you could say that these actions are considered...selfish....

It all makes sense now.
Monika may be selfish and jealous, making her an enemy in Sayori's eyes, but she's not the only one who's head she's coming after.

I'm sorry to say this, Sayori fans, but Sayori hates YOU.

Think about it. In all those other visual novels you're given the means to mess with people's hearts to get the ending that makes you most satisfied. You have a lot of power in these games.
But DDLC is different in the fact that you have no power. Regardless of what you do, the story will go on the same path. Regardless of whether you accept or reject her confession, she kills herself anyway. These are all examples of how DDLC makes the player feel powerless against the other forces in the story.
But there is one particular example I want to highlight. At various points in the game, if you try importing a save file and loading it, the game will simply go to a black screen, where Monika calls you out for "cheating." But just because she's there, doesn't mean she's the cause of the problem. If what I said earlier is true, then this must be another attack by Sayori.
If anything, it mirrors the other two attacks she made which involved the girls killing themselves. Sayori causes a problem which the game does not know how to respond to, and it's up to Monika as president to clear up her mess. Just as she dealt with Sayori's suicide at the end of Act 1, she also needed to step in and act as a handler for these 'cheating' scenarios so the player can still continue playing the game. After all, if the game just breaks then Monika can't talk to you anymore, can she?

So now you know what really goes on in the mind of Sayori. Depression plagued her life to the point where it felt like injustice, and it soon turned into hatred. Hatred for the two most powerful entities in the game world playing her and the other girls like puppets on a string. She had two powerful enemies which needed eliminating, and what better way to get rid of two enemies than to have them turn on each other? And that's just what she did throughout the course of the game.
You turned on Monika, just as Sayori had planned.

But as a final thought, this makes the ending even more disturbing. Because, in a roundabout way, Sayori won! Monika tried as best as she could to stop Sayori from hurting you, but only ended up making it worse. Once Monika had been deleted, Sayori has access to all the tools necessary to finish off the player. But in a suprising turn of events, Monika came back for one last hurrah. One final attempt to save you.
And what does she do?

She finishes Sayori's work for her without even knowing.