Even in the first chapter, I got the impression that there was more going on with the bully situation than they were letting on.
- He claims that the guy "started bullying one of his classmates out of nowhere"
- The main character "fell down the stairs" while he was with the bully and wasn't pushed or anything
- Bully is super dejected that Miyu doesn't remember him
My guess is that there was a huge misdirect in chapter 1. The initial "bully victim" likely did something to deserve it and the bully got pissy because the main character intervened. For whatever reason, the bully didn't want to reveal why he was bullying the first girl and just let the main character believe it was just a random victim, but started acting coldly to him. Then the main character threw himself down the stairs to injure himself to get the bully in trouble (and in chapter 1, he wasn't going to hit the bully, but himself again like Miyu did). After that, the bully spent the next year harassing the main character for it and just ran with the story that he switched victims.
My guess is that "Miyu" had also sent him some threatening texts or something after hearing the story, which is why the bully is looking at his phone when he's talking about how he wants to start bullying Miyu in chapter 1.
EDIT: Looking back in the first chapter, he's staring at his phone the whole time he's suggesting that he gives him nudes of her. I get the feeling Miyu is the one who texted him instructions to stage that whole encounter, saying they'd be friends if he did it (and he'd get the nudes as a bonus). She was planning to entrap him somehow and had to resort to plan B when the main character refused, which is why she randomly pops up in the classroom out of nowhere.