We didn't all choose to give our word, and she did choose to stir up violent anti-human sentiment. Frankly, I couldn't care much less about her say in the matter while her presence is a threat to the students.

And it isn't so simple as a "proper path" or whether they're "good" or not. They've got an agenda, but they also have more legitimate authority in this than we do, and we may have to rely on their backup in other matters again someday. They aren't an enemy we want to make.

[Hijikata's word and honor are priorities, but they rank somewhere far below the safety of the school and its students to him. He's, at his core, a somewhat vicious pragmatist.]