I reread the first two volumes and I feel like I understand the characters a lot more, eg, the whole thing with Isunama.
In terms of Naoi motivations, here are some quotes.
Chapter 1, when she starts harassing Kurumi:
"Compared to someone like you who seems so perfect, I must be utterly beneath you."
At which point she is all smiley. Later on in the chapter when she punches Kurumi who collapses:
"I like it, y'know. Watching someone who can do what I can't, who seems perfect, writhing around like a bug."
Then, when Kurumi starts laughing while smiling, Naoi looks disdainful like with Kuduo and calls Kurumi a freak. In chapter 2 Kurumi is back to looking overwhelmed rather smiling and Naoi is back to being smiley most of the time. Conclusion: Naoi is finds it gross for someone to be smiling etc in these situations. That's presumably what she dislikes about present Kuduo, whereas she likes how Kurumi becomes overwhelmed and quiet.
After this, when she looks disdainful to Kurumi, it's always because she's annoyed by Kurumi suffering to meet other people's expectations of her. This is when she starts to identify with Kurumi and like her more seriously, rather than seeing her as entertainment.
Chapter 4 we get the "When was the last time I was this excited to go to school? No... This is the first time," which I interpreted her as comparing Kurumi with Kuduo.
In chapter 6, we get to see her abusive dad, who blames her for her mother leaving them. She acts disdainful and indifferent again. Conclusion: People who look down on her remind her of her dad. She likes to use violence to regain her dignity in these situations, so that she is no longer "below them" but the one in power. This being something she has in common with her alchoholic dad is probably something she is all too aware of.
Then, in Chapter 9, Kurumi tackles her into the pool to recover some papers and tells Naoi there is nothing between them. Afterwards, Naoi is thinking about in the park:
"What do you mean there's no us? ... I don't care. If I'm just killing time, anyone will do. That's right, that girl Isanuma seemed fun."
So here she is essentially planning to continue going through haughty girls, using them as a source of fun and entertainment. My reading here is that she had this type of relationship with Kuduo, essentially using her to try gain a sense of fun and self worth through violence. This likely would have been one of the most positives relationships in her life at the time. Kuduo eventually being that desperately into it would have taken away that sense of power, as she was now just conforming to what Kuduo wanted again. That, combined with Kuduo not coming to school, would have led to her trying to find it elsewhere with Kurumi, back in chapter 1.
At the end of volume 2, we have Kurumi suprise Naoi by telling Isanuma off, at which point Naoi runs off with a more self actualized Kurumi. That brings us to Naoi's current arc of trying to figure out who she is, what type of relationship Kurumi wants to have with her, and what she wants in this situation. The part of her that likes feeling powerful and sees violence as a valid method to get what she wants has largely been lying dormant, but likely is still there. Probably there is not really any issue and it will be fine when Kurumi and Naoi talk to each other, but Naoi would be having a lot of fears and self doubt for the time being.
Edit: Then in chapter 14, we see the flashback where Naoi's mom tells her that people who retaliate with violence are the same as the person who started it. She then explicitly asks Kurumi if she resembles her dad - she likely feels like she was abandonded due to being similar to him.
Later she is happy Yoshizawa/Kurumi is also socially isolated. Naoi places her hand on Kurumi's neck while thinking about that she can't leave Kurumi, which she is doing while Kurumi is asleep. I think that's really driving home that she feels like she is hiding this part of herself and trying to act like the person she thinks Kurumi wants, but only expects it to last until Kurumi finds someone better. She believes she is playing along until she gets abandonded again.
Then, of course, Kuduo shows up again, which has been discussed plenty in this thread.