It's easily forgotten or missed, but she didn't simply have a crash out because Kaya is difficult. She encountered a ghost directly while trying to deal with Kaya and it broke her.
She was breaking down long before that if you read her notes. Ghost was probably influencing to accelerate but she was already on her way for mundane reasons. Not as big of one probably but she would have eventually snapped and said something awful to a child, at best.
The other teacher says it in the nicest way possible because Japan is a very non-confrontational "don't rock the boat" country. "Sense of responsibility" = "her self-esteem depended on making children behave" and "personality clash" = "her personality is fine when it comes to children who behave but when there's a "problem child"..."
Someone who had a full breakdown over a child like that should have never been let back around children but management re-hired her. I think it's been at least alluded if not outright stated that they're having a teacher shortage? Which isn't a good reason at all to let a threat risk back but.... management is thinking about business more than childcare.
