You're trying to take women's rights from females by denying them a way to uniquely identify themselves.Rights are not a zero-sum game or some kind of exhaustible resource; I have no idea what you're getting at with this.
I challenge your contention that "a way to uniquely identify themselves" is a right of biological women or other groups. Never heard of any such right; it sounds totally made up.
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The meaning of words is what all people agree on. In the US, marriage used to mean a legally recognized union between a man and a woman of the same race. Otherwise it was miscegenation, or sodomy. Then as times changed, they added a qualifier: "mixed marriage" or "mixed-race marriage". Same thing happened in the last decade with gay marriage. In both cases, it eventually just turned back into marriage again.
You disagree that trans women are women. Fine. Activists are trying to make the case that they are; that womanhood encompasses more than being biologically female, and same for manhood. A lot of people agree.
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You say that everyone could identify as black-descendant-of-slavery to access scholarships. I say you are making a laughable category error. (Did people start marrying their dogs after Obergefell was decided? They did not.)
The reason someone identifies as something other than their birth gender isn't well-understood, but it is fair to say that hormones and the development of the brain play a significant role in the way people think and behave. Hormones have strong ties to sex and gender. They have very, very little to do with race. Category error.
If non-black people started identifying as black to claim their piece of a societal debt to the ancestors of slaves, they would be (and have been[1]) ridiculed. Most people don't try this, because the vast majority of society agrees that is not acceptable.
[1] https://en.wikipedia.org/wiki/Rachel_Dolezal