My gender is nonbinary.
I don’t mean that in the “I identify as nonbinary”, “my gender identity is nonbinary” or what have you. I mean that in the standard “sex is the anatomy of your reproductive system, while gender is the social roles generally associated with particular anatomies” sense.
Strangers mostly see me as male, until I open my mouth, in which case I’m usually read as a gender-non-conforming female. Most of my acquaintances don’t know what my assigned sex at birth is. (I don’t exactly make a secret of it, but they have no reason to care, so why would they bother to keep track?) My friends are carefully selected for people who either see me as nonbinary or are very good at pretending.
Of course, I’m cognizant of the privileges that allow me to live as a nonbinary person. My partner is happy to support me financially, which means I don’t have to get a job with people who misgender me. I have a remarkably trans-positive social circle, one in which I can find many people who see me as my gender. I have physical features that make it relatively easy for me to appear androgynous (which include, of course, my privilege as a naturally thin person). I am a very lucky person, and if a couple of things hadn’t gone as well as they did I wouldn’t be in the situation I’m in now.
But it’s still true: I don’t live in the world as a woman or a man. I live as a nonbinary person. And I am so thankful for that every day.
I guess this is what they mean by “gender is a social construct”– that is, gender is a thing that exists because people believe it exists. Of course, most social constructs aren’t very amenable to changing via someone wanting it hard enough: it’s not practical (nor desirable) to convince everyone that money is meaningless or the government doesn’t exist.
But.. if I claim loud and long that I’m nonbinary, then people come to believe I’m nonbinary and then I actually am. Through nothing but the power of my will and other people’s goodwill, I can bootstrap my way into being nonbinary. I glared at society hard enough and it socially constructed me a gender more to my liking.
It’s a heady feeling.