When we define sex as genitals and gametes, we're reducing people to their genitals and gametes.

How is it reductive? What else would you define sex by, but sex organs, chromosomes, and gametes?

But people are more than what's between their legs, so should we not define sex as genitals and gametes? Should we not say someone is "male" or "female" because it would mean they are defined by what's between their legs, which is ... "rude" and "offensive"?

Unlike "vagina owner," "prostate haver," and "menstruator"?

Given there are intersex conditions in which intersex males have uteruses and intersex females have testes, wouldn't it mean testes, penises, etc are not male-only organs and females can have them too, and uteruses, vaginas, ovaries, etc are not female-only organs and males can have them too?

Not by your own logic. How are you defining "male" and "female" in this sentence?

parrotfish and clownfish

It's really cool how much variation there is in nature. But it is also entirely irrelevant to human sex and the human construction of gender identity.

Are your hormones and secondary sex characteristics not part of your biology all of the sudden?

Right, medication and surgery aren't an expression of your biology.

But you don't have to be an anarcho-anything. This is about basic freedom of expression: Why should I have to express myself as a man when I prefer to express myself as a woman?

What is a woman?

Intersex people are far more common than statistics would tell you with bonus points for GRS performed on visibly intersex newborns for decades and many of them will never know about it.

And what are intersex people? What are the two ends of this spectrum? How would we even have a category that is "intersex" if there weren't the discrete categories of male and female?