Well that's exactly it. Isn't the argument that a person may feel as though their brain is a particular gender, and that the physical characteristics of their body represent the opposite gender. I can imagine, being quite comfortable with my own gender, that this would be something of a nightmare.
You're right, they cannot change their gender, for that is seated in their brain. And so they're changing their body, which certainly can be modified, to match.
Why is this a bad thing, if we accept the initial argument?
If their 'brain feels' a particular gender different from that of their body then isn't that by definition a delusion?
Gender isn't like ethnicity, where its driven by self identification. Its more like species.
Theres a similar continuity of species where membership of a species isn't black and white, much like I posit for gender. However, the point where an individual is on that continuum isn't something they can change by wearing different clothes or getting cosmetic surgery. Same with race.
Suppose I was part Asian, say my great grandfather was Asian, but the rest of my ancestors were European. So on the continuum of race I'm way over the European side but not all the way. But I 'feel like my brain is Asian'. To look at me you would think I was European. This makes me uncomfortable; I want people to look at me and think I'm the race that I 'feel in my brain'. So I get cosmetic surgery to make me look Asian such that if you were to look at me you'd go "Oh an Asian guy". But that wouldn't make me Asian, would it?
I have no problem with such a person, or a 'transgender' person, wanting to get cosmetic surgery to feel more comfortable in their body. I just hope it works out and they don't feel like a disgusting mess afterward and kill themselves because they can't really get their penis reconstructed.
Where I draw the line is the distortion of the concept of gender or race so that it becomes like something you can 'dress up like' and change. I think that this is where 'sex change' or 'gender reassignment' surgery is being misrepresented to the people to whom it is being offered. Its a fraud.