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I totally get what you mean. I thought I had it figured out, but then I wasn't sure.
The way I understand it, the older guy (jaehyun) that we see the girl (nayoung) with is a family friend or something of the like and he had a boyfriend that isn't around anymore and the cat (ran) reminds him of the boy. And I thought the high school stuff was a flashback at first and that jaehyun was the boy (hanseo) in the high school scenes, but then I realized the girl (nayoung) is wearing her high school uniform with jaehyun and ran as well.
So, in short, what I've gathered so far is that nayoung is the girl in the high school and the girl at the writers apartmant. She wants to help the cat boy speak and she wants to understand what happened to him and the writer seems to be struggling with some memories of a boy that he loved that looks like the cat boy. At the school, it seems like nayoungs friend hanseong likes her and spends time with her mom and the blond chick is shifty af and likes hanseong. I think she's gonna tty something shitty to fuck with nayoung. It also seems like nayoung is distancing herself from her friend to avoid trouble.
Sorry If I missed something!!
I don't know if it's because I'm not used to this style of drawing, but I don't understand what's happening and who's who. It doesn't help that I have so much trouble remembering Korean names. If maybe someone could give me a brief summary of what's going on, pretty please? Oh, and is the stuff happening in the school happening at the same time as the thing with the cat or is it someone's memory?