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Most likely any attempt at specific, verifiable definitions would be insufficient for their fascistic purpose. A biologist, Forrest Valkai, covers well the complexity involved when defining the social construct of sexual differentiation in a measurable way in the video Sex and Sensibility. Hence, the laws reliance on "reproductive role" while simply assuming some unstated definition of "biological sex".

It’s probably specifically because they wanted to punt the intersex issue to the court system. Talking about chromosomes is too specific and measurable. Talking about sex in terms of being associated with gametes makes it more subjective.

I have a friend with Androgen Insensitivity Syndrome. She’s a woman, has always been a woman, is married to a man, and has two adopted kids (AIS means she’s sterile). She has XY chromosomes.

Is someone going to walk up to her and say, “Sorry, ma’am, you’re male now”?

Her gender assigned at birth was female. She was raised as a girl, always identified as a girl, and had no idea anything was different until she started having health problems at puberty.

Because they aren't interested in doing so, and know that there are no good ways to define these things.

What they want is the means to impose strict gender norms, and to persecute anyone who does not fit for any reason and in any way.

So, today they want workers who aren't super gender conforming to provide their birth certificates to use the restroom. Then they'll escalate until workers conform or get shoved out. After that, strict gender dress codes for all employees, then gender-specific roles... sometime down the line, a ban on married women working in state organisations, women unofficially barred from most workplaces & most roles, and ideally barred from being out of the house without a male relative as chaperone, blocked from having a bank account or owning property, and in due course... welp now they are property.