There's a big difference, Steve, between me not being good at explaining something and you not understanding. I started to read my comment to someone before posting it and even before I was done the portion you found so difficult, they said, "This is just semiotics." For you to understand, you'd have to first want to understand. If you were in a classroom with a professor, would you just keep saying that they were bad at explaining and keep arguing with them? Or would you ask even one question? The arrogance and pride you're putting on display is sterotypically masculine. Like, you just went on and on with an argument about an interpretation you weren't even sure was accurate and then, in fact, was not.

The part you thought you understood correctly before losing the will to live? You missed the most important point. The point everything hinges on:

At some point, MAYBE, "woman" was a word that only meant "adult female" with "female" being defined as someone with a vagina, etc. But then behaviours and roles started getting adopted by women in such pervasive numbers that they became associated with the word "woman" exclusively, such that women could be identified by these things, now because they were symbols of the first definition: the vagina-etc. It's called "transitive property."

If all women (A) have vaginas (B)

and all people with vaginas (B) have long hair (C)

then all women (A) have long hair (C).

If all A are B, and if all B are C, then all A are C.

This is a valid argument form in formal logic called Hypothetical Syllogism. You can keep adding more features to it. If all women have vaginas and all people with vaginas have long hair and all people with long hair wear skirts and all people who wear skirts are nurturing then all women are nurturing.

A long time ago, so many behaviours and traits and roles were given to women, taken on by women, so exclusively, that the word "woman" literally came to mean THESE THINGS TOO. Such that, through transitive property, through symbolism, we can see them and connect them to the word "woman." And what happened, then, is that the word "woman" came to take on more and more associations and symbols.

And now people want to insist that this isn't true, this isn't relevant, and the word only means one thing. Even though, when they use "woman" they are not even able to know the biological information they say they are implying with "woman." They can only guess. Through the implication of transitive property.

The law of transitive property requires the word "all". And we now know that "all" is not true when it comes to all people who look like women having vaginas or ovaries. Not only because of intersex people, who are as common as redheads (https://isna.org/faq/frequency/) but also because of trans people. Because many trans people "pass" as cis. Therefore, when you refer to a stranger as a "woman" based on how she looks, you're just guessing. You don't know. And that confident assumption, that assumption of the transitive property, you can extend that to trans women, too. That's what they're asking for. Not to be defined as "this kind of person who has a vagina and ovaries."

If the "bleep" metaphor was too complicated, I don't expect this to have helped and without you humbling yourself and asking a question, I can't or don't want to help any further.

Babies are assigned a gender at birth. Gender is not sex.