A fast way to learn is to teach. When teaching, you see what is not known by the pupil and instruction and demonstration is presented to empower the student to mastery. However, it is likely that the student’s  instruction given can be applied to something applicable to teacher need of mastery.

True. The teacher’s mastery may beyond the student’s. True, also, that the teacher’s failures can, by applying what was taught to the student, also  become the focal point of the teacher’s study and mastery.  Of course, any mastery simply leads to the next level of failure in seeking perfection.

Thus, it is: A teacher learns as much from each student, each of whom  is to be thanked.