Your post reminds me of a student I taught in private school who attempted to correct me EVERY SINGLE DAY I taught him. He would question comma placement, alternate spellings of words, opinions that he considered factual, etc. Occasionally, he was right--and he was quick to snicker and gloat--but I usually had to politely explain why he was wrong. The other students in the class got sick and tired of his high-handed attitude and insulting manner as much as I did. Unfortunately, he had many weaknesses in English--unreadable handwriting, constant misspellings, run-on sentences, below-level reading and learning comprehension, etc.--yet instead of trying to better his own deficiences, he chose to try and correct the teacher. I sure was glad when he moved on to the next grade so I wouldn't have to deal with him again.
Teachers are not perfect: As one of the previous posts mentioned, humans make mistakes and show their emotions just as other people do. An experienced teacher will try to remain calm and patient in the classroom, but it's not always possible. I lost my temper most often over repeated disciplinary problems by students who had been warned and punished for the same misbehavior time and again. When administrative practices are weak in this regard, students learn quickly that they can exceed certain boundaries that most people--and especially adults--would not breach.
As for mocking a student, I had to bite my tongue many times to not mock the student I mentioned earlier. Teachers are adults, and they should recognize that mocking students is both unprofessional and immature as well as cruel. As for fact vs. errors, teachers should always be careful not to give incorrect information or exaggerations to a classroom full of students who are sure to be influenced in some manner. You will run across teachers in both high school and college who will exhibit deficiencies of some sort. I have had several college teachers (part-time adjunct teachers) who were so poor in their classroom manner and teaching techniques that I wondered how they were ever hired in the first place. As a student, you will have to learn to deal with this sort of problem; if you recognize a conflict immediately, you should attempt to switch classes and take your chances with another teacher. Sadly, educational practices are not without their faults, and no teacher is perfect.