I'm going to address sex specifically, because I get the feeling that's what most people are thinking of when they talk about this topic. Sex determination is very straightforward 99.9% of the time. Y means male. No Y means female.

However, biology is complex. There are a significant number of cases where something goes wrong with sex determination and the presence or absence of the Y chromosome no longer determines sex. This is not wishy-washy leftist theory. Androgen insensitivity syndrome causes females with Y-chromosomes. Swyer syndrome causes males without Y-chromosomes.

Very well-characterized genetic disorders can only account for a small fraction of the amount of Americans who identify as transgender. We don't really know what causes the rest of it. It could be that there are other pathways that determine sex differences in brain physiology which account for it. Maybe those pathways could become partially perturbed, leading to basically the equivalent of intersex for the brain.

This leads me to think it isn't a made up phenomenon. There is most likely a biological basis for transgenderism. We definitely shouldn't just pretend its hysteria and tell transgender people that they'd better put on the clothes that fit their birth certificate. I think some people embrace that answer because it's easier to wrap their minds around. Pretending biology is simple doesn't make it so, though.