It's very difficult to understand any of it. I don't know what feeling like a woman means, or feeling like a man, come to that. This is partly because identity is so complex and contradictory, and also feeling is a kind of snapshot in time. Right now, I feel hungry, and I'm wondering what's on TV tonight, So that's my identity right now.
So if a trans woman says she feels like a woman, I don't know what she means, but obviously, she has the right to say it. And if someone says you're not a woman, also OK. Then what, I don't know. I think it's an Indian veggy assortment for tonight, (food).
Another point - feeling is different from description. Hence, I would probably be described as male in the third person, but I might feel differently from that. A lot of the arguments stem from the switch from first person to third person.