"Trans" women are no more a 'subset' of women than '3-sided squares' are a subset of 'triangles.' Men cannot become women; males cannot become females. Left cannot become Right; True cannot become False. Life is largely established as antitheses by the Creator.
You're right. They are more a subset of women in the way that squares are a subset of rectangles. And if you want to imply that they aren't real women you'd need to put the quote marks around the word "women" not to word "trans".
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After all, only men are able to become them