I once took a Geometry class through a long proof with the class agreeing on each step. By the end of class we had proved some really wrong things but the class still kept with me. Finally one student said "Mr. Freedom, this can't be right." Next we asked where the mistake was. (It was quite early in the proof. The premise was that a=b, at some time the equations are divided by (a-b) since division by zero is undefined, lots of phony things occur. I had hoped that students would become uneasy at obvious untruths on the board, but they accepted it for at least 30 minutes, getting farther and farther from reality each minute.)
The point was that teachers are not always going to tell students the truth, they should be capable of understanding and critical thinking. They felt that they had been betrayed. (But I believe they were always more on guard after that.) And no, I did not usually stand at the board and talk all period. I don't know about this teacher, she seems loopy and lazy due to the kid's presentation but she may also have been capable of teaching, there simply is not enough data to tell her level of sarcasm.