Thank you for showing me that my thoughts on gender can be unclear when I focus on one aspect.
To me, based on a lot of reading, gender identity is not gender in and of itself but an aspect of gender. Gender identity is how the brain processes information about gender and that is determined by certain brain structures. This has been shown in a multitude of research studies.
However, gender itself is an interplay of gender identity, biological sex, sexual orientation, romantic orientation and culture. These are all separate threads that we weave together to create a sense of self. In that way, gender is actually a very individual experience because no two people are going to create the exact same tapestry from those threads.
The idea of what a man is or what a woman is comes from culture, not gender identity. We know this because different cultures have different ideas of what makes someone masculine or feminine and individuals follow the cultural template they were raised in.
I believe that gender identity is how the brain is set up to process that cultural information. We know that humans are highly social creatures and a large part of our brains are set up to process social context. We have entire classes of neurons that are devoted to creating a theory of mind of other individuals. Those of us who have a brain set up to process and emulate masculine input will identify as men and take in the cultural context of what a man is. The same can be said of women.
However, we also know that the brain tends to be a mosaic of male and female traits. We have studies that show that parts of the brains of men and women have different average sizes or densities. But when we look at the individual, we see that their brain does not fit neatly into the male or female category. The most womanly woman will have parts of her brain that fall closer to the male average than the female.
It is my belief, and I admit that I could be wrong, but it is my belief that it is this neural mosaicism that gives rise to non-binary people like myself. Our brains are not set up to take in information from one side of the masculine-feminine divide that our culture perpetuates, but we take in and emulate information from both. We know ourselves to be somewhere in the middle. I also believe that there are a lot more people who fall in the middle than we realize.
To sum up, I don't believe that there is an essentialist explanation of what a man or woman is. It's too complex. Researchers from different disciplines give different answers to that question. I believe we need to embrace the individuality of gender and that is the perspective from where I write.