To advance your point, the ability to bear children is kind of the definitional distinction from which all of these biological distinctions derive as well as tons of social distinctions. Race has no such analogue.

What about infertile women or intersex persons?

How about cat vs dog?

I'm not following.

"the definitional distinction".. ?

I don’t know what point you’re making, but my “definitional distinction” remark meant that “sex” is more or less defined by the ability of one group to bear children (fertility issues aside, of course). Not sure if that addresses your concern.

There is no "concern". Think about the other part of your comment rather than the gender bit. Good luck.

If you insist on being unclear I'm not going to work to tease out your meaning. Have a good day.

No, between the two end of the gender spectrum, there is all kinds of shades of grey, starting with persons with intersex genitals and all the way up to women with a more male personality, body hair and so on.

Nature doesn't care about categories and will happily produce all kinds of distributions. It's us humans who try to bin them cleanly.

Intersex conditions are disorders of physical sex development, and the specific disorders themselves most of the time sex-specific. It is a physical medical condition, and they certainly do not create a spectrum of sex: There is not a third or an inbetween kind of breeding setup, just bugs in building the proper things. Bugs that are insanely rare.

Women with more male-like personality goes into that "variation in a shared system that has sex-linked distributions": There are women that have more typically male personality configurations and the reverse, just as there are tall and short people. Nothing surprising about that, and it doesn't relate to sex itself being a binary dictated by two different reproductive mechanisms.

Sorry, you are falling for a category system that is entirely human-made. Nature doesn't care about "disorders" but produces the whole spectrum. Nature doesn't even care about that the evolutionary fitness of many variations is zero.