Too many teachers assume if they admit they were wrong, the students will get more insolent, as if sensing weakness. I’ve briefly been an assistant teacher in a middle school, and I found that on the contrary, students seem to appreciate an earnest admission of mistake and calmly accept the apology. Even some students that would be insolent in other situations. When it’s clear you’re wrong and the student knows it, pretending you’re right won’t do any good. Acting in a respectable manner will get you more respect.