The paper telling everybody that Kyou kissed Yuuta and that's why he can't come to school anymore, and that nobody should be friends with him, had the same flower design as the letter that she sent to her friend later. So my interpretation was like Kyou's saying "I kissed the boy we were both interested in, and you made me a social outcast until we moved, and I thought that was the end of it". Though I guess there's the question of how the mom found out, or if Kagami did even more than that.
She's definitely got some anger bubbling underneath that ditzy nice girl surface. And apparently she's been holding a grudge for like 10 years, because Kyou stole her first crush? God help Kyou if she finds out what else he's been up to with Riki, lol.
OH SHIT, okay yeah I missed the stationary being the same, thanks! I was wondering why the letter was highlighted and only focused on the name haha. Hm but yeah you're right about the mom thing too, it feels like the class had just read the letter since the twins didn't have a chance to even go back to class yet after the school metting, so it couldn't have been that same letter that prompted the meeting to happen. Whoever told the mom, perhaps it just wasn't important so it wasn't addressed.
And Kagami is definitely been pretending like everything's fine but hella doesn't trust Kyou anymore for that, which I guess is... that makes sense I guess. Must've been a huge shock, since she both admires and relies on him, yet also realised that she can't trust him anymore. Pretending that something akin to betrayal didn't happen isn't exactly healthy for their relationship as siblings, and ngl, Kyou didn't exactly wait for kagami and Rikimaru to break up first like he's making it out to be in this chapter, so even if it was 10 years ago, he's still doing The Thing Kagami was upset about. Even if society is being unfair to Kyou, he's also being unfair to his sister. And even if she got hurt first, Kagami really went nuclear there huh.
I like Kyou, but just like Kagami, it feels like they're both desperate for their love to work out, even if they hurt each other in the process.