That's the advantage of subjects like mathematics, where a theory is either true or wrong and does not have any facets in between (except simply not knowing which one of both it is). Here, it's entirely normal for a student to point out a mistake the professor has made during the lecture, and the professors are totally cool with it. All that counts here is if your argumentation is logical or not (and if the premise of the argumentation makes sense, obviously), and while personal opinion may play a role in whether the professor is more inclined to believe you beforehand or not and some people may be more stubborn to insist on their view, it's not what counts in the end. Obviously, this doesn't mean there are never any discussions in mathematics, boy do they happen and still, sometimes a professor or tutor may not recognize a proof or argumentation you're absolutely sure of. But usually, the only thing that counts in the end is still logic, and I love that.
-Gata