Most of the answers I've seen have been way too philosophical.
IM-not-so-HO, the most important reason is that we are social animals. On a psychic level, we can barely even exist except in relation to other people. (Consider the effects of solitary confinement, shunning, or long-term physical isolation.) We have an inborn need to be seen for who we are, and the parts of us that we cannot allow to be seen tend to atropy or fester. That's the principle behind mind control: if you force a person to convincingly act as if s/he believes X for long enough, s/he will end up actually believing it -- the actor become the role.
That's why we need for someone, at least -- a friend, an SO, a therapist, the denizens of CD.com -- to recognize this part of ourselves, or else we'll go crazy. It's not even necessary for them to approve, just to know that they see it, even if they say we'll go to Hell for it. And for some of us, one person is enough. For others -- well, that's what Jerry Springer's show is for
(YMMV, of course. I'm sure that there are _some_ people out there who crossdress, or do other things, which they are perfectly happy to keep forever secret from the entire human race. They make great spies.)
