Why do teachers have to be the brightest?

To play the devil's advocate here:

It is not uncommon to notice that seldom to the best athletes make the best coaches. It is also common to note that many of the most successful professors in terms of publishing and research simply are not good teachers.

As such, why is there such an emphasis on seeking the brightest for the teaching profession? What advantage would they be in the classroom? Has anyone ever done any research into the relationship between being a good student and a good teacher?