The only person One should ever compete with is Oneself. This life we live is to live it always bettering ourselves. As we do, the world will follow (or not, yet that is okay, also).
"You are to become a creator; not a competitor; you are going to get what you want, but in such a way that when you get it every other man will have more than he has now." Wallace Wattles
EDIT: The teacher should teach well enough so the student no longer needs him. That is the ultimate goal of a teacher. If one continues to depend on the teacher, the teacher is not doing their job properly.