If you don't mind, I'm going to tackle this in the form of both an argument and a bit of a little story... It makes it easier to follow, I think?
Be L'il Fukawa. A person who is ignored on a good day and hated on a bad day. This child is like an egg, that will one day spawn the hostile and defensive Fukawa we know today. But, tell me, what do we know of this egg? What can we see about Fukawa's life from her ingrqained mentalities?
Let's start with her friendships. We can tell she didn't have many, no, that the concept is basically alien to her from how she reacts to Naegi calling her one.
Fukawa wrote:
Huh?! Wh-What did you just say?!
That's genuine shock and surprise, her irritation after only further hammers home the amount of disbelief she feels. There's an even better way to see this.
Kokoronpa! I don't think it's in the english versions (or maybe it is?) but Kokoronpa is an event that can happen if you're good enough friends with someone in which you have a literal debate/crross-examination of their innermost thoughts/feelings. That's right! For once, you can literally read
Fukawa's thoughts!
Fukawa wrote:
Why does Naegi…. Keep spending time with someone like me…
He’s getting my hopes up for nothing…
That's not an act, that is genuine self-loathing. But more than that, is the fact that we can tell from that second quote that Fukawa DOES want to be friends. After all, you can't get your hopes up for something you don't want, right? In fact, Fukawa has basically based her life, her becoming an SHSL writer, around a few kind words from a teacher. How desperate for, well, kindness must you be to devote all your energy to something from a few kind words.
So, let's get back to L'il Fukawa. She's got no friends, despite the fact that she does want them, and is hated... Oh? Hold on. I'm wrong. She DID have a friend. The boy who would go on to be her first love... However, he was leaving to another town. The one person who had ever been kind to her... Fukawa realised it was now or never and confessed to him with a note.
Dangan Wiki wrote:Being too shy to tell him in person, she instead wrote him a letter. The next day, Toko found said letter mounted on the bulletin board, believing it was the boy's way of making a mockery of her. This was confirmed to her when she talked to him again and he said he hated talking to her and was always made fun of because of it.
Be Li'l Fukawa. Be crushed. No-one was ever your friend, in fact, everyone hates you. But more than that, and this is important,
being friends with someone hurts THEM. That's right, being friends with someone doesn't just hurt you, it's also something which simply destroys their lives too. Hell, this could explain her relationship with Togami. Someone who doesn't care about her, could never be hurt by her, right?
In any case, it didn't just metaphorically ruin this boys life. No... It literally kills him. This is where we introduce the most important factor of the Fukawa story. Enter, Genocider Syo.
I find it's implied simply from Syo's nature and description that they killed this boy, Fukawa's one "friend". In fact, the wiki confirms this to be true.
Dangan Wiki wrote:At some point, Genodice Jack chased the boy all the way to Shikoku and killed him.
Now, considering that Genocider remembers things that Fukawa doesn't and vice versa it's safe to say that Fukawa didn't come to the realization that she had a serial killing split persona from the start. Instead, she probably came to standing in front of her former friend/crush nailed to a wall and dripping blood.
Syo's Profiling Results wrote:The culprit stayed at the scene of the crime for a long time, but also [...] they escaped from it in a state of aggravation.
So, Fukawa had to piece Syo's existence from her blanks in memory and her suddenly appearing at the crime scene. After all, the fact that she was trying to lock herself in after Chihiro's death shows that she both worked it out, and wanted to avoid it happening. I can imagine she felt guilty, afraid... With her non-stop self loathing the sheer amount it must have weighed on her, the guilt and hate, would have been enormous.
Be L'il Fukawa. Anyone you fall for will die. Anyone who befriends you will have their life ruined. Becoming friends with people will hurt you. You have a monster in you, and it keeps getting out...
Touko Fukawa is a hostile, self-loathing creature. She's hostile and defensive. But, hell, that's the only way to be. When befriending you will literally kill them at worst, or ruin their life at least... Maybe that's the only way to be. So, yes. Fukawa is self-loathing and rude, but to some point, it's arguably a defense mechanism. Arguably earned, even!
By being how she is, Fukawa is protecting both herself and "everyone else".