Sigh, it was expected. But it's still infuriating.
At this point, he must have a trauma about people in power (not necessarily a joke, given the few hints of his backstory). As it was pointed out to him in this very chapter, he talks the talk about how important his students are to him, but doesn't walk the walk. If a person of authority (a more prestigious teacher or principal) enters the picture, he bends over backwards for them instead of siding with the monster girls.
Aria isn't ignorant ignorant or rash. She knows what she wants. The other school may be better, but the prinicipal is a jerk and she prefers being with her friends. Washio better start listening to her.
