What's the point of gender reassignment surgery which doesn't change a person's chromosomes?

The single thing that does determine sex is the SRY gene. Its discovery in 1990 changed everything science thought it knew about sex in placental mammals.

Corollary: sex and gender in humans is actually floridly-complex and occasionally very messy.

This can include the SRY gene being defective, being blocked by other mutations, being on the X chromosome instead of the Y, or missing altogether.

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It doesn’t have to change chromosomes, because chromosomes do not determine sex.

It’s usually found at the tip of the Y chromosome (which is why we thought sex was in chromosomes), but there are a number of variations that will change a person’s anatomical sex, neurological sex, chromosomal sex, and genetic sex.

So what happens inside “gender-affirming care” depends upon the patient’s lived experience. However, it’s been demonstrated conclusively by a century of psychiatry trying to change transgender patients’ gender identity to match their physical anatomy does not work and in most cases only worsens their mental health, especially in minors.

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All of these variations have an effect on the person’s neuropsychology and thus their experience of their sex & gender.

In other words, these different levels don’t always sync-up. It is possible for your brain, your body, and your genetics to have different biological sexes.