I think now we are arguing about how one would define transgender. It is important to note that I could not give less of a fuck about the idea of 'gender' beyond its use to describe a person's sex, so instead lets use the word transsexual.

In my view, if a person has a brain irregularity that causes them to feel dysmorphia, and that their body would be correct if it has the opposite sex's characteristics, that is proof enough to me that transsexualism exists.

Scientists cracked open the heads of people who had in life expressed this dysmorphia, and they found an irregularity in a part of the brain that differs based on sex. I consider this neurological basis of transsexualism reasonable evidence that the dysmorphia truthfully exists, outside of a purely mental delusion, and that they would truthfully feel better in a body that was more similar to the sex they believed they should be.

I see no harm in a benign procedure that makes these people more comfortable with themselves. Sure, they are not -literally- the sex that they want to be, but they now have a body more similar to what they believe it should be, and that belief of what it should be is what they call gender.