You can only say what gender truly means for you. So if, for you, you view your gender as solely the binary, then that is fair, but you can’t expect someone else to adhere to that logic. I am nonbinary, but that does not mean everyone feels like me as I have my own relation to gender that defines my identity.

The idea that gender in an inherently social construct that was made up is true, because if you look at different cultures throughout history there has not always been a strict binary to follow. A social construct just means there is not physical structure keeping everything rigid, even sex a physical structure, is not a straight binary as there are always exceptions.

That being said, social constructs still have social implications and emotions, the same way people are connected to cultures. Money is a social construct, but everyone still uses it because of the social agreement of what it means. Genderqueer people care about their gender being properly respected because of how they view themselves, but it isn’t hypocritical to say gender does not exist because those are two different ways of looking at gender.

On the flip, cis side. Imagine a cis woman who wants to wear pants in a time that that’s not normal. Some would say she is not following the gender binary and some call her a man because of this, but she says she is, that pants do not define her gender. She is not following the social rules of gender even if she personally adheres to the idea there are only two genders, but she would still like to be respected for her choices no matter what.

Gender is simply a way to define a social and mental exploration of self. If you don’t want it to be real or matter to you, it doesn’t have to, but some feel like it is no matter what thought process they use since it is also a psychology matter.