I'm a decade older than that, and I've managed to wrap my head around it. Since we're on a forum dedicated to a fantasy story, let me run you a hypothetical:
If a meddlesome wizard transferred your mind (I'm assuming you're a dude here) into the body of a woman, you'd still think of yourself as a man, right? You'd still have the same thoughts and self-perception, at least for a while; you'd still be you.
If you can accept that, then you've accepted the idea that physical sex and gender don't always have to go together. From there, it's a small step to imagine people who feel like that all the time, often from a very young age—who feel, very strongly and firmly, that their inner self doesn't match their outer body. People react to this in a lot of ways, from surgery to hormones to dressing differently to cutting their hair to nothing at all, but whatever they decide to do it's polite to treat them as the gender they want to be treated as.