Sex is about reproduction. We're an anisogamic species, which means we reproduce through the production of specialized cells with half the DNA (gametes) of different size. Male individuals are the ones who produce small gametes (spermatozoon) at some point in their lifetime, and females are the ones who produce large gametes (ovum) at some point in their lifetime. When a spermatozoon and an ovum fuse to form the zygote, the normal amount of DNA is restored. Some species are hermaphrodites, which means they can produce both male and female gametes. Humans are not hermaphrodites, though. In humans, there are several genes involved in the process of sex determination, but one of the most important is the SRY gen. If this gen is present, then the embryo will develop testes. If not, then it’ll will develop ovaries. The hormones secreted by the testes drive the male differentiation pathway for the rest of the male reproductive organs. And the absence of these hormones drives the female differentiation pathway. As the SRY gen is located in the Y chromsome, XX individuals are females and XY individuals are males.

All of this remain true despite that sometimes things go wrong and some people are unable to produce gametes, or only can produce anormal gametes or a lower number of gametes than normal. People who have a disorder of sexual development (DSD) are rare and they are still either male or female, i.e. they don't produce a third type of gamete.

Humans can't change their sex. Neither naturally nor with the help of medical technology. There is not such sex change. What "medical transition" can only do is to create a simulacrum of the opposite sex through exogenous hormones and cosmetic surgeries. However, every one of your cells keep having the same sex chromosomes you've since conception not matter how much exogenous hormones you take and not matter how many surgeries you undergone. Just because some people undergone gonadectomies, it doesn't mean their bodies weren't/aren't built around the potential capability of producing a certain type of gamete. Although hormones and surgeries may affect your fertility, you don't suddenly start producing the gametes of the opposite sex. BTW, both males and females have the same sex hormones. The difference lies in the concentration levels of them. Also, the hormonal profile of females is more complicated because it varies through our menstrual cycles and through our different life stages.

Contrary to what TRA say, we don’t need to examine someone’s chromosomes or gametes to tell their sex. Secondary sex characteristics don’t define sex, but they are usually a good way to tell someone’s sex. We have evolved to be able to tell the sexes apart. If we weren’t able to say who kind of humans are able to get pregnant and what kind of humans can impregnate the former our continuity as species will be quite complicated.