My interpretation of the story as told is the teacher owes your son an apology.

Your son acknowledged his inappropriate behavior, and apologized. The teacher then pressed the issue further, making an argument that was dead wrong. It is not acceptable for your son to be continued to be dressed down by an authority figure in this manner (I assume in front of all his classmates). Your son defended himself from the unfair charge, and the teacher escalated her own inappropriate behavior in response.

This is band class, not boot camp or the police station.