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.