Ok, some do, but I know dozens, if not hundreds, of math professors. I don’t know any that I think became math professors so that they could teach. That doesn’t mean that they can’t teach; it doesn’t mean they don’t like teaching.
Think of professors like musicians. Becoming a professor is – or should be – like becoming a professional musician at a high level of ability. Some outstanding musicians like to give lessons. Some like to teach music to kids, adults, anyone who wants to learn. Some only want to teach master classes. (By the way, not too many of them want to teach people who say, “Do I really have to practice?”) But some don’t want to teach, period. If they have to, they will. Some will do their teaching job responsibly and some won’t.
So, that is the lowdown. To paraphrase Mark Twain: The problem with professors is that they are just like the rest of us.