But it isn't just a vagina that makes a woman. They have specific organs that require specific hormonal profiles. Women have different skeletal dimensions than men, to the point where sex can be accurately ascertained from the skeleton alone.
The physical differences between men and women are not just societally imposed, and form the basis for their oppression. This cannot be wished away.
By the same logic a white person could claim they were actually black. The reality is there is far more genetic distance between a male and female than between races.
Yet, anyone who did such a thing would be seriously problematic. It is equally problematic for a man to claim he is woman by exactly the same logic as the oppression against women cannot fairly be appropriated by men.
Men have been screwing over women for thousands of years. It's not ok for them to appropriate their name and identity because of some qualitative feeling they're experiencing. It's not ok.
What's wrong with the term "transwoman" for a transwoman?
The physical differences between men and women are not just societally imposed, and form the basis for their oppression. This cannot be wished away.