I am astonished that there seem to be some on here who think that the teacher should not have intervened in an unpleasant interaction involving name-calling because they too think the pupil is crazy.
I and many other pp have said over and over again, that if this was about children being unkind and picking on or behaving badly towards another individual then of course teachers need to step in.
The teacher could and should have explored what had happened (she comes in all guns blazing, only a fool does this in hearing one side of the tale with kids), she could and should have talked about how the conversation made the other party feel and why that's not great and then discussed with them how to resolve the issues and how to move forward from here. Maybe with some thought as to apologies or agreeing how they would interact with the other party from this point. She could and should have listened to the girls. She could, if she felt she was right, have explained the basis for her intervention and decision making and ensured they understood
She did none of it. Do you honestly think the other party was well served by this interaction?