From time-to-time a question of the form "My professor said $X$ is true, but my book says that $X$ is false. Is my professor wrong?" is asked. For example, I've seen questions similar to:
Question 1. My instructor said in class that every continuous function is differentiable, but I just read in my book that the function $f(x)=|x|$ is continuous but not differentiable. How is this possible?
I'm surprised to see comments and answers stating "Your professor is wrong". While it's true that if the professor made this statement, then he/she is wrong, I'm not comfortable with automatically accepting this assumption.
It seems very unlikely that a calculus instructor would make such a statement. It seems overwhelmingly likely that the OP in this example is incorrectly recalling something the professor said. I try to communicate this in my comments and answers with statements like "It seems unlikely your professor made this statement, as the example you give is a famous continuous function that is not differentiable. Are you sure your professor said this?"
While healthy skepticism is important, I've noticed that many (especially younger) students tend to search for excuses for their misunderstanding of a topic rather than admit their misunderstanding and address it. Therefore I think it's important to communicate this (without discouraging students from questioning statements they think are false).
I'm curious if others think this is as important as I do and how others deal with questions of this form.