Erythronium
Yes, to answer your question, I am a woman, a regular born one. I don't really understand concluding that because my reaction to things doesn't look like yours, I don't take them seriously. I find people who are disingenuous make me angry, and people who I feel should know better, but don't, make me frustrated. Some topics, like the environment, make me feel something like despair. But I don't see getting angry at people who have errors in their thinking as something that would be useful - it happens to me sometimes, I expect it does to everyone on occasion, but not usually when discussing something like the meaning of language or whether a particular idea is factual, or rational. I am usually a relatively phlegmatic person. In any case, for people who are deluded, I don't think getting angry helps them see. For those who are not deluded, getting angry doesn't help either.
I can easily see why someone else might have a different sort of response to this topic, but I am pretty committed to the idea that it is not a good idea to be less than careful and precise about these kinds of discussions.
I don't think it is the case that people never use the term subset in relation to people. I don't think people use the term at all much, because it's only useful occasionally. And as this discussion shows, a lot of people don't really know what it means in an exact way, so they might not use it at all.
But the idea that it shouldn't be used for people because it likens them to objects - to me that is something that comes out of thin air. A set can be of anything, ideas, people, animals, molecules, numbers, angels, whatever you want to talk about. It's useful because what it describes is the relation of the things you are talking about - in a context like this one, I think it could be particularly useful in that it does the opposite of what a lot of people seemed to think - it does not imply that the relation is about anything in some fundamental way being of lesser or greater members - it's completely about the context.
As for using the historical marginalisation of black women - sure, they are in a way. But as you say, it's not inaccurate or offensive to see that the historical experience of black women in our culture is particular, and that is what the idea of subset is referring to. I don't think it would necessarily be offensive to compare that to some other marginalised group - we do often compare the struggles of one group to another, or a situation in a particular context, and I think we all understand that they may not be identical, but the comparison can help with explaining something.
I think this feels very wrong because of the attempt to compare people who have a lot of cultural privilege, to people who don't. But that really isn't about the use of a logical term to talk about groups, and it obscures the real issue to say so.