I don't understand, given all of the above, how such a term can be seen as offensive. I am consigning you to a subset of your gender rather than your sex.
The fact that you've just "given all of the above" is the offense. To accept the usage requires accepting a whole heap of misogyny.
Specifically:
- the "taking it for granted that society associates" these men with women. We don't, and society clearly doesn't because they don't get treated like women at all. They're treated like Very Special Men You Can Never Say No To. For "trans ally" men, they often find it hard to conceal their "bros before hos" glee about supporting men doing "womaning" properly, and the opportunity of unleashing a whole heap of invective on women who don't comply.
- Claiming that these men are women. "By definition", no less!
- Saying we have "trans women" now meaning "men who say they're women" (with a new definition of women) rather than "women who say they're men".
- "Your gender". Did you just assign us a gender? How are you determining women's gender is the same as a trans-identifying man's? Are you only paying attention to what's in the mans' head here?
If your usage didn't do all that - if by "cisgender women" you meant "women who don't claim they're men", and "transgender women" you meant "women who do claim they're men". there would be (at least to me) much offense involved. It would just be in-group language separating sex focussed around the "trans" group. But as it stands, it's extremely offensive due to the redefinition of "woman" that goes along with it.
'Female' and 'woman' are sex and gender respectively, right?
And going back to this - clearly, no. They're an adjective and a noun. It's clearly not workable to consistently use only an adjective for one meaning, and use only a noun for another, as you can see in general usage. They end up being flipped between as if they're thesaurus alternatives, without meaning distinction.
I've only ever seen "transgender female" used in the press as a synonym for "transwoman". We've long used "trans-identified female" here, in an attempt to be clear, but in the world that says "trans women are women", "female" is routinely used for males.
You're trying to claim a compromise position that's already been demonstrated to be unworkable - neither "female" nor "woman" are being reserved for actual women.