During a conversation after a recent violin Master Class, the visiting instructor (CC) described what he looked for in a student:
You have to be really great at something. Not great at everything, but at least at one thing. I'm a good enough teacher that if you've got problem areas I can help you fix them. But if you don't know what it feels like to be great --- well, that's something I can't give you.
(see also MusicMaster (4 Jun 2001), ...)