You're the one who is not listening. You compare people wanting to have a sex change to someone wanting to go into the army. I'm sorry, but that's just ignorant.
I've known a number of transgendered people, and they all knew from early on they were "wrong." In the reading I've done on the subject, and the interviews I've watched with transgendered people, no one's ever said "you know, I always felt like I should be the opposite gender, but then I just got over it one day." I've also never seen anyone say, "oops, I wish I hadn't done it." Does that mean such a person doesn't exist? No, they might. But the majority of these individuals went through hell most of their lives up until they went through the change, and after the change they felt "right" for the first time ever.
The reason so many people think it is wrong is because they are just as ignorant on the subject as you appear to be. Many people find the whole subject of gender reassignment as disgusting or wrong, so it's not much of a stretch to find they don't agree in this situation with her decision. Someone who has never felt this way can never understand just how terrible it can be for these individuals, and if an operation like this can help them feel normal in their own bodies, then why should they be denied that?
And this young woman is not the youngest person to have her gender changed--she's just perhaps the youngest who's ever done the full-blown hormonal process. Doctors have had to perform the procedure on younger children because of biological problems.