Do people not know what a fact is these days? This is not at all scientific fact in any sense of the word. What you mean by a “man is a man” is actually “my idea of what a man is, is a man” and these two things are not at all the same thing.
What you’ve stated is not an argument on facts, it’s one of semantics. It’s like me saying “a hotdog is a sandwich” is a fact and insisting on it. What I’m saying is “this hotdog fits my criteria for a sandwich” but my wife is going to disagree with me. Language and communication is not a fixed space.
This is totally regardless of whether or not you believe the science behind gender ambiguity which is a whole separate argument. You are arguing that your categorisation is somehow inherently “the true” categorisation like the mathematics of the universe, and it is not, semantic categories are man-made things. Other societies have three or more gender categories. What do you do then? Who’s is the correct one now?
If what you’re actually saying is that “I should be allowed to categorise people however I want, and insist they fit into my box of what I consider to be X” then well… we’ve seen how unhelpful that shit is to society and I don’t want anything to do with it.