"the distinction between male/female and woman/man is a scientific distinction"

I don't think that is true. The scientific community has identified biological traits that are correlated with males and females. I don't think that "woman" and "man" are not scientific terms - I think they are social terms. Also, "gender" used to be synonymous with "sex", but socially we have started to distinguish between these.

Scientists agree I believe that there is no such thing as a "male brain" or a "female brain" - rather there are characteristics that correlate with males and females, but everyone is an individual, and people can vary a-lot. I believe that I have a brain that highly correlates with females, but I am a male because of my reproductive biology. And that is not a problem for me - I am very comfortable with who I am - I feel no anxiety about it.

"seemed to be missing an essential point."

I will be interested to know what that is. I am not easy to convince though because it has been a long time since I have heard an argument that I have not already considered. I am waiting for someone to share a perspective that shows a flaw in my logic. As I said, I have been in a great number of these debates, and if I am missing a key point I very much would like to know.

And again, I am supportive of trans rights, and see trans people as people. I am not antagonistic. I am supportive; I just don't agree with a particular narrative that the trans community maintains. Trans people are people. I wish them all well. I would come to their defense.