This may be splitting hairs, but that just seems like describing the way in which it’s wrong. If your friend describes a transman as a “woman”, they know or should know that it will give you the wrong idea of who you’ll find on your date.
I’m reminded of the doctor in Arrested Development who says of a patient, “it looks like he’s dead” when what he means is that the patient literally looks like a dead body because he’s covered in blue paint. There is a sense in which what he said is true, but the expected understanding of the statement is false. So too here.
This seems like the wrong question, and as a corollary it suggests that I’ve framed my argument poorly.
Language is about shared understanding, the meaning of a word is the ideas it conveys, both for the speaker and for the listener. My argument here should have been that speakers who call a transwoman, “woman” mean something like what we mean when we call Siri “female” or use the words “she” and “her” in relation to it. Instead, I tried the stronger claim that this is what “woman” already means for the whole speaker population, which isn’t true. Rather, the majority of the speaker population already has multiple meanings for female pronouns, some of which apply to biological women, and others of which apply to things that don’t have biology. The stronger but more modest claim is just bridging the gap between people who are using the same word to mean different things.
So, when you describe the use of “woman” to describe transwomen as “delusional” or a “lie”, that isn’t correct where you and the speaker agree on all the underlying facts and just think that “woman” is a better way to describe that person than “man”, i.e. they intend to convey true information and reasonably expect that description to most accurately convey a true impression.
I expect the objection will be along the lines of, “why not just say transwoman?” And in some situations that’s a real option and the best choice. But that isn’t always the case, and we should be careful, with something as fraught as gender, in assuming that the only impediment to using transwoman are those that are explicit (e.g. on a form that gives you the option of describing yourself as “man” or “woman”). “Men and women”, “boys and girls”, “ladies and gentlemen”, “men’s room and ladies room”, these all convey a complete dichotomy of humanity, and strongly encourage a choice between one bucket and the other.
It doesn’t take a lie to think that, when confronted with that choice, two people who agree on all the underlying facts nonetheless disagree about which side of the dichotomy a person will fall, when those people are using different meanings of the words “man” and “woman”, “he” and “she”. No one needs to be delusional, and assuming that only delusion explains it is uncharitable. Someone can say truthfully and clear-eyed, “I don’t fit either category by their traditional definitions, but if I’m forced to pick, it is X that fits best”.
As for the emotional reaction, I feel like it doesn’t take too much empathy to understand it. People are almost always the local expert on themselves. If someone suggests that, with everything they know about themselves, “it is X that fits best”, to say otherwise is to say either 1) “no, actually I know you better than you know yourself”, or 2) “no, actually I know the meaning of words in your native language better than you do”. Neither of those is particularly flattering, and both seem pretty likely to be wrong.