I learned flatpicking and fingerpicking at the same time because I wanted to BE both Roy Buchanan and Leo Kottke. Eventually, I grew up (I'm 46).

I start all my young students with a flatpick unless there is a specific directive from the parents to start with classical studies, but that's very rare. In any event they get fingerstyle a little later, depending on their progress, though I start them without a thumbpick. If they want to try a thumbpick it's okay with me (I use a Fred Kelly Slick Pick), but young hands have trouble with fit and control in my experience. The serious students want to try everything, especially if they think it puts them ahead of the "competition". It's my job to reveal to them a variety of styles and approaches to music and guitar, and (like mooman, above) it makes my job a lot more fun.

Peace, Mooh.