Doing something doesn’t mean you can teach it, and vice versa.
Playing flawlessly doesn’t mean you’re an amazing teacher.
TEACHING: SCIENCE OR ART?
But teaching is an art itself – it takes practice. A PhD Math Professor must be really good in math. But it doesn't mean that he's a good at teaching. He could speak alien and makes everything complicated that it needed to be. It's not about what he said, but how he explain things. Kids aren’t widgets, teachers aren’t robots and everybody loses when we treat them that way.
Not every college graduate is cut out to teach, regardless of his or her innate intelligence, G.P.A. or previous career success. Only those with specific talents and training become gifted teachers who, working with a talented mentor teacher and a variety of tools and learned techniques, can motivate students to want to learn.