I think I'll just let Stephen
have Quote of the Day before lunchtime:
[W]hen a student challenges a professor, it's business, not personal. Part of personal development is learning where the limits are and whether or not they are credible. One simply has to learn to say "no" very pleasantly and stick to it. (I don't get paid to prepare my notes, I don't even get paid to check the marginal conditions in my research. I get paid to say no and to enforce standards.)
I have many young faculty now, with the department shepherding its Vietnam-era faculty into retirement. Some are good at saying "no", and a subset of them can do it pleasantly. Sadly, I have to "mentor" the ones that don't come off as pleasant, as the rest of Stephen's post explains.