Sometimes the ring is the best place to learn humility. It sounds like this kid is severly lacking in that department, when his own coach/teacher is telling him he's not ready. One of two things will happen,
1. He gets his a**ss stomped and comes back to you, at which time you tell him I told you so and than decide to let him back in your school or not.
2. He wins and feeds his ego more and leaves to train somewhere else, which from the sounds of it would not be that bad.
It's up to you but usually guys that pigheaded won't listen to anything, so your probably better off without him there. My two cents.
"The hero and the coward both feel the same thing, but the hero projects his fear onto his opponent while the coward runs. 'Fear'. It's the same thing, but it's what you do with it that matters". -Cus D'Amato