Oh I'll admit I'm wrong either way, but yes I do not like my authority to be challenged. It makes the class significantly harder to manage when students feel like it's OK to dunk on me at any opportunity and provides a bad environment for learning. My preference would be respect, but I will settle for being treated with respect. If a student won't offer it to me with their questions, then I won't offer it to them with my response. But I will always admit they are correct (if they are).

Authority that cannot be challenged is authority that cannot be respected. Authority must continually earn the respect of its constituents, or it will lose its power over them.

I sort of agree with this. In a classroom, you can challenge me, my knowledge, my abilities. I like to think I earn the respect of my students with all of these, as well as my compassion, my fairness, my humour.

The reality is that I am an authority however. I wrote the assignments and the exam and I mark them too, and I do it all in accordance with the state-mandated curriculum. If they "know" something because they read about it elsewhere, I should be treated as a equally valid source of information because I am. I know the curriculum inside and out. They dont "need me to admit that I was incorrect, and move forward with the correct information", they need me to tell them why the thing they "know" is not the thing I'm teaching them. I offer that I was incorrect out of humility, not necessity.