(later edit for clarity's sake, when I originally came out to my girlfriend it was as the cross dresser I thought I was, the realisation that I was transgendered came later. This seems to be a well worn path.)
Let me explain. I am 6 foot 8 inches tall. As a girl I wear a UK size 18 dress, but my feet are UK size 15. It's an over-used cliché about transgendered people that they are born in the wrong body, well in my case in a very cruel joke from the creator that's more literally true than for others. A long dress is mid-calf on me, a knee length dress is mid-thigh and a short dress is positively indecent. As it happens I'm in proportion. I may wear a size 18 but my height means I look a lot more slender than most size 18 women and years of walking and cycling mean that my very long legs have a shape most women would kill for. If I could easily buy a set of size 15 heels and I topped off my ensemble with a suitably bouffant wig, I'd be comfortably over 7 feet tall. Cool in a dominatrix-trashy-drag-queen kind of way, but hardly unobtrusive.
If you are of average height, you are fortunate in that you are merely a face in a crowd. You are unlikely to have experienced being significantly different from the rest of that crowd so you will never have been really noticed by that crowd. Try dyeing your hair pink for a week, and see what a difference it makes. The average man in the UK is about five feet 9 inches tall while the average woman is about five feet four inches. I'm a foot taller than most men and sixteen inches taller than most women. As a man in the street, I've had people openly staring at me, I've been the butt of more unfunny height jokes than I'd care to mention and from time to time I attract unwarranted open hostility from people who feel threatened by me. Being tall is not without its advantages, for example violent behaviour rarely comes my way, but a tall transgendered woman of my height would be nothing but a freak in the eyes of the general public and would not be able to pass unseen. It takes a lot of courage for any transgender girl who can pass in a crowd to take her first steps in the open and I admire those who do, I simply do not have what it takes to go out as a girl with very little chance of passing unseen.
I've had a lot of time to think on this subject, and I've concluded that there can be some surprising upsides to this. It is not without regret that I recognise being unable to pass as a woman means I can never consider transitioning, however having that decision made for me by my physical size means that I will never have to face making it myself.