Trans women do exist. They are indeed a subset of women.
Trans women do exist. But they are a subset of men. They are men who want, imagine themselves to be, or live in the sex roles of, women.
Unless you believe in it as a religious ideology, there is no such thing as a gendered soul that is somehow living within the body as the opposite sex to the body itself. There is zero material evidence of the existence of an opposite-gendered soul, or any soul. It is a belief, not a material fact. People are and live in their bodies as part of the material world.
Some people want to be the opposite sex to the one they are born as. That’s fine. But they aren’t the other sex; and hormones and surgery don’t change them into it. We all know this; and most people are very happy to allow for a legal and social fiction that transwomen can “live as” women, and trans men can “live as” men, and support them in doing so.
We don’t want to be told, however, that reality is not reality, via made up terms that pretend things aren’t as they are; or language changes that pretend something is true when it’s not. That’s ideology and religion - compelled belief - and not compatible with a progressive, democratic, secular, rights-based society.