I find it surprising how many crossdressers don't know why they do it. It seems simple to me. Your brain is part female, and that part of you wants affirmation that you really are female. It is a "yes, you are really a girl" security blanket for your inner girl. For most of use, the male part of your brain also wants affirmation of being male. Trying to satisfy both sides can be a bit confusing.
You could also ask why anyone likes anything. As intelligent beings, our brains need more than just basic survival needs. Intellect is a complex thing, so the interests can be complex as well. Nobody worries too much about why they like or dislike certain foods. People are just different. When it comes to harmless activities like crossdressing, don't worry about it. People with the urge to be violent or pedophilic have a serious problem and need to figure out why. Crossdressers should be happy that they are interested in something fun and harmless, and just enjoy it.