Something being a social construct doesn’t mean it doesn’t matter, especially in this society where your gender is a thing people want to know about so that they can form opinions about you. It is also a way of self expression because with your gender you can signal to the outside world how you see yourself and how you want to be.
If you are forced into a role that does not reflect who you are, you are going to have a rough time, because people automatically assign you traits and how they will treat you based on that role. And then it doesn’t matter if gender is a thing imposed on us by nature or something we invented to categorize people.
I’m not sure if this helps but I hope it does at least a little.