I'm not persuaded. I believe a man is what a man does, that whether or not one calls it "gender," behavioral differences between men and women account for the sense that one belongs in one category or the other. Absent those differences, it's not clear to me what a trans person is sensing. Either way, I think the TERFs' fear of trans people follows my line of thinking, even if it is a non sequitur.

You do indentify as a man, because saying you are one is "identifying" as one. That's what the word means.