Be thankful that was their first response and not "Oh sure we'll do whatever you want!!" 21 is very young and the problem is that if they operate and your hair-loss progresses even more aggressively, as it so often does in young patients, you might end up looking like a freak with an island of hair in the middle of your head. Go see what they have to say, I think that the initial reaction to be reluctant on their part is a very good thing.