Earlier quoted context omitted.
> I'm talking about biological sex (which implies gender, No, it doesn't. Gender (which is distinct from both sex and gender identity, though there is an increasingly popular modern view that gender should be ascribed based on gender identity) is a socially ascribed trait, and different societies have recognized different numbers of genders and used different methods of ascribing them. > The vast majority of cases yo…
The facts are that if your chromosomes are XX you're female, and XY you're male. This directly affects things like strength, size of organs, behavior, and more. Anything else is just mental issues. There are inherent differences between men and women whether people want to admit it or not, biology doesn't care about someones feelings
Then we have the world of chimerism, ie a person with two set of chromosomes. Genitals of both sexes may be formed.
Then we have mixed gonadal dysgenesis, also known as X0/XY mosaicism.
dragonwriter mentioned XX male syndrome.
Those are just a few big ones. We then have some lovely research into gender identification through sex differences like the size of organs, brain tissue and so on. Works great, except when you do it with transsexuals. For that group the measurements predict the gender they say they are and not their chromosomes. Those studies are used as evidence that transgender is biological, not psychological.
The human body is a complex analog system, and in complex analog systems there aren't much binary 1 or 0. It is more like a scale which leans towards either one direction depending on the sum of a lot of factors. What we call male is just the state when the sum of those factors point in one direction, female in an other. Occasionally you get scales that balance between the two that you can't actually say where it leans.