The argument against using the words like that, is that now there's no word for "adult human female", unless we want to create/use the new-ish word, "ciswomen", but a whole lot of "adult human female" type women, especially it seems older ones who were present for the hardest battles for more equal rights for women, really resent having the very word "woman" taken away from them, by fiat, by people who are usually either biological males, or men of some sort, or by relative children.
It feels audacious to me as a 41 year old to tell a 60 or 70 year old feminist "You are no longer called a woman, if you're referring to anything biological males can't also be, too. The word woman now specifically does NOT mean a majority of the things it meant for your whole, long, feminist lives, and it does not any longer mean having the common female anatomy and distinctly sex-specific traits and customs of necessity which are exclusive according to nature itself to biological females. You now have to call yourself a "ciswoman" if a uterus, or a baby living for a year or more off milk you alone produce, or any of that stuff is the type of woman or aspect of womanhood you're talking about. If you don't like it, get over yourselves."
So, I'm going to let other people use the words woman and ciswoman however they see fit, and give them no grief about it, as long as they don't pretend to not even be aware of the fact that there are two distinct and different definitions of the word woman (reflecting two distinct concepts, one of which is crystal clear, and the other one which is as hazy as a ghost, to be completely honest) now in use.