Yes, the purpose of those chromosomes is to contribute to reproductive roles, of which our species has two. However, that's not
the same as gender or sex. Gender and sex are both social categories, not objective observations. You can objectively describe someone's chromosomes or sex organs. But labeling
these structures as male or female is merely cultural.
But being transgender is not
a psychiatric problem. It's considered a biological variation in sexual characteristics, just like being intersex. Scientists know that sex chromosomes, sex organs, and secondary sex characteristics tell only part
of the story. We still have an incomplete picture of how sex is determined by the body, and the fact that some people are transgender shows we have a long way to go.
This isn't "some argue," it's "experts agree." As I've repeatedly pointed out, experts on this subject agree that hormone therapy and/or gender confirmation surgery are medically necessary
for many trans* people. There's simply no alternative treatment.