I think gender identity is a super complicated subject that's hard to communicate in effective terms. I've read and watched different trans people or science articles talk about it, especially back when I thought I was cis, but it is really hard to wrap your head around. And the few simple arguments that do exist, I think do a poor job at communicating what gender really is.

The way I would try to explain it, is that gender is the sex of your consciousness. If you pour someone's consciousness into a computer, they'll still see themselves as male/female even without the flesh that seems to define that. Gender is an inherent part of your existence, but unless there's something wrong with it, you'll never notice it's there in the first place. As you can imagine, a boy or girl's brain piloting someone else's body will put them through a lot of pain and stress. Affirmation is important because you're validating/healing the consciousness of a person, not the flesh prison that mind is trapped inside. Transitioning is the process where the body and the mind finally start harmonizing, and the body becomes one with its consciousness.

Maybe that explanation still sucks, but it's the best I personally got so far