Depends on how you view it and your definition of "woman". There's a lot of discussion out there about what "woman" means I won't rehash all of it (e.g. ability to have babies, physical attributes, clothes, emotional feelings, etc.). People use the terms that they can relate to, and sometimes others understand that relationship and sometimes they don't.

All I know is that when I'm presenting as a woman (As I defined it, dressing as woman, putting on makeup, etc.) my personality (naturally expressing myself, being emotional, talking about feelings, being joyful and fun) is accepted and rejoiced whereas when I express this similar natural way when I'm presenting as a man, people find it unappealing and/or ignore me. So I present as a woman socially and more and more. I live in the way them I'm appreciated more and have more connection and more fun.

I can't explain it, I didn't create this situation, but these are the facts in my personal experience. So I might conclude that I must be a "woman". Maybe yes, maybe no, but in terms of who makes such a "decision", it's definately in the gray area, and depends on what terms one uses and what they think those terms mean. Plenty of men say they feel like a woman, they don't mean they feel like they can have a baby, they mean a whole variety of other things, each person is different.