They killed his adopted parents too.
Now Ayato knows some people have to die. They won't stop from being beaten down. And since he has the skill to kill people, all he has to to do is be taught how to be an assassin? That sucks for him.
That teacher might be nice and have a moral attitude, but his backstory has to be dark if he's teaching kids how to murder.
No matter what "good" intentions they have for him, that school is just gonna end up manipulating him into doing things he does not want to do.