This is the part I have a problem with:

Gender is a category assigned by the individual

Gender isn't assigned by the individual. Gender is assigned by parents, doctors, the community, and society broadly. Gender is an inherently social construction. Some people have misconstrued this to mean that gender is an individual construction. It is not. How you see yourself is only part what makes you, you. You are also defined by how others see you. I understand that some people don't identify with the gender that has been assigned to them, and thus want to change their gender assignment, and I empathize with those people, but whether or not they are able to do this is at least partially out of their control. Just because you see yourself a certain way, doesn't mean others will see you that way, and, again we are defined not only by how we perceive ourselves, but how others perceive us.

Gender isn’t assigned by the individual. Gender is assigned by parents, doctors, the community, and society broadly. Gender is an inherently social construction.

Social/cultural construction doesn't mean that it has to be a collective construction.

Your gender is not different from something like... being a nerd, or being a fan of star wars. Someone might call you a nerd, but ultimately it's up to you to embrace that label or not.

And anyway, cultural things like gender, being a nerd, etc is absolutely unrelated to biology.

Social/cultural construction doesn't mean that it has to be a collective construction.

It absolutely does mean that. We just live in this age of hyper individualism, where people attempt to atomize the individual from the collective, as though the individual is something wholly its own, but it isn't. It's not possible to separate the individual from the collective.