I don't know how I forgot about Imposter Syndrome. I have certainly felt it. When I got to law school I thought for sure that I would probably be pretty horrible. But it turned out a lot of people were even worse than me. :) (But certainly many who were simply brilliant.) Then I got into my LL.M. program and I thought, OK, now for sure. But nope. Did you even feel that way towards the end of your Masters?
I felt it towards the end of my Masters, I felt it when I got accepted into the Cleveland Institute of Music with the best scholarship that my teacher had heard of for a bassist (and she worked in the scholarship office for a while early in her career), I feel it every day. I know one guy who I consider to be the best bassist in North America, if not the world, and he has routinely considered quitting because he can't live up to his own expectations. I studied with him at a summer camp over two summers. I'd say it rubs off, and maybe it does, but I was like that beforehand, too.
Apparently Eric Clapton seriously considered quitting the guitar after he heard Jimi Hendrix.