As with pretty much all of these questions and answers... this is how it feels for me.. I know most of my CD-ing friends in real life agree with me, but the world is bigger than that.
With that disclaimer out of the way: why the desire to go out? For me, after taking the umpteenth bunch of photos with a tripod and the self-timer.. I got bored being indoors! While I'm huge geek (love to read, play videogames, etc.) for which I usually stay inside, I love doing stuff outside the house. I love to go shopping, I love to go to movies, love to go to restaurants and bars and have beers or cocktails. Why wouldn't I also want to do that while being dressed up?
My brother and some of my male friends (most of them dress like slobs though.. ) put on a nice suit if we're going out to dinner, my female friends put on make-up and wear dresses. I like to wear dresses.. so why wouldn't I sometimes wear them while going out?
I admit there are/were other reasons as well... it's also exciting, I get compliments, "can I get away with it?". Like mentioned above.. it's also about validation. For me, it's not just about wearing the clothes, but also feeling free to express myself in whatever way I feel at the moment.
Mind you, I'm 36.. and I feel completely comfortable in my male body (though I hate hair.. so I'm having that permanently removed).. don't want to transition or anything. However, when I dress.. I do want to present myself as what I think is a good looking woman. So yes, breast forms, the occasional corset and hip padding will be there when I go out in the world.
I'm sorry if this sounded a bit rant-ish.. but I sometimes get a bit miffed when we get into the whole "no true Scotsman" thing about crossdressing. Everyone's situation and desires are different.