I think that there are a good number of people who don't entirely feel comfortable in their own bodies, or feel somehow out of place, so it's clear that something is going on. As to if "wrong brain/wrong body" don't really know, think it's probably more a matter of a chemical imbalance, or a genetic coding thing.
I think too though, some of it is the emphasis that society puts on certain things - that certain people have to act in certain ways, or that if you are a particular gender you are supposed to look/dress for that gender, or you can only like certain people, etc.... If we were more open and accepting, I think that we'd have less people feeling like there was something wrong with them.
I had a friend of mind who came out of the closet and says he always felt like a woman! They say God doesn't mistakes but here is a guy that tried being a man and stopped because he hated being this way! Because I know him I'm at odds over this! Thank you