I'm not trans. I'm cis. But I don't deny the obvious fact that a trans men can have a period. Because, well, blood.
The moment that we agree that a trans men exist and that they can have periods, periods stop being exclusively female.
And as a woman I can tell you that my period doesn't define me. I would still be me if my period stopped.
So the problem is not that I want to define you. I don't. If you want to say that the period is what make you who you are, it is OK by me. But period doesn't make someone a woman and neither lack of it makes you not a woman. It is a fact.
But you are trying to define trans men and me by saying that if you have a period you are female and if you don't, you aren't. Period is not inherently female. It is not. Is just a experience some cis woman and trans men have in their lives. And some intersex and some non binary people. Period is just a biological process, but doesn't define gender.