This is an interesting thread.
I think BarbieJellyBabyBrain has it more-or-less right about the ‘sub’ in ‘subset’. But there may be more. Let us see.
‘ A set A is a subset of another set B if all elements of the set A are elements of the set B ’.
It might be simpler to see what it is all about if we use the equivalent definition
‘ A is a subset of B’ means ‘if x is a member of set A then x is a member of set B ’
[equivalently, again, ‘A is a subset of B’ means ‘if you are A then you are B’ … think of membership of sets in terms of having properties, roughly speaking, so for instance if A is the set of green things and B the set of things that look like cabbages, then ‘A is a subset of B’ means ‘if you are green then you are cabbage-looking’.]
Now, the ‘if … then’ here gives us the clue that ‘subset’ language is a way of expressing logical inference. (Set theory has the same structure (‘is isomorphic to’) simple logic.)
So, translate into logical language:
‘black women are a subset of women’ means ‘if you are a black woman, you are a woman.’
That ‘ if you are a black woman, you are a woman ’ is a weird thing to say. Why? And why might we think it racist even to assert it? (Is it not – obviously! – true?!) I suspect it could appear racist for me to say it in certain contexts because asserting it might seem to presuppose the possibility of debating its truth – which presupposition would be racist: it is not open for debate.
No debate is familiar, of course. And TRAs want to claim ‘no debate’ for what to them seems an equivalent assertion: ‘if you are a trans woman, you are a woman’ … or, equivalently, ‘trans women form a subset of women’.
Once the meaning of (the relative neologism) ‘trans woman’ is explained, however, it becomes clear that trans women form a subset of men, not of women. By definition, a trans woman is a man who wants to be (or perhaps believes he is ) a woman. ‘A man who …’ If you are a trans woman, perhaps surprisingly until the neologism is explained, you are a man.
No debate? No, perhaps not. (Unless we locate the debate where it belongs, at the level of understanding the semantics and the logic. Are those debateable? Hmm.) But the TRAs have the case (in technical terms) arse-over-tip. Trans women are men. No debate ; it is analytically true that trans women are men.
Why such an interesting thread? Several reasons. Not least that it highlights the difficulties inherent in arguing and explaining exclusively in writing like this, particularly with regard to matters of logic. What would take a moment or two of face-to-face interaction can take a long time on the internet. So I find, anyway. Twitter does not help. I suppose that goes without saying.