
Okay so the teacher is concerned with the accident topic because he may be the cause of the black haired guy's death, that's why the black haired guy holds a grudge against the teacher, and that's why he was summoned in the first place by the green haired girl, because they both resent the teacher. That's my theory, not necessarily right tho..

No. The sister never accused him of causing an accident. She has always accused him, however, of not CARING about what happened to Yuki. I think it more likely that the teacher simply did not intervene because he either did not know there was bullying going on, did not know how to stop it or didn't want to intervene because he still had the scars from what happened to him in the past, albeit unintentionally.
This is a good one, I'm eager to see how it goes