There is nothing random about self-determination. If I asked you to identify your gender, would you flip a coin? No? Neither would a trans-person.
And I'm sorry but here we just reach a base disagreement.
Totally internal labeling that doesn't relate to anything external is by definition meaningless and I don't think I'll ever understand the fascination bordering on fetishism that Progressivism has developed for it in the last few years. "I am because I say I am" is... just not meaningful absent some other criteria.
I don't "identify" as a gender, I just am one and that's based on actual objective criteria, not on some purely internal "sense of self." I'm male because I have a specific genital and chromosome structure, not because I "feel" something or "identify" as something. I no more "identify" as male then I identify as 5"10, blue eyed, or O Positive blood type. I just "am" those things. I could tell you I "feel" like I'm or "identify as" 6"4, brown eyed, and AB Negative with the same degree of meaningfulness to me. I could say I want to be those things, but me just saying I am is... well like I said if you call a tail a leg a dog still has 4 legs, not 5.
"Otherkin" are as perfectly valid as Transgenderism if you're treating self identification with this degree of absoluteness. The language is identical and the language is the only thing you're pointing at as mattering.
Again since I don't recognize any purely non-biological distinction between the genders as valid "identifying" as another gender is absolutely meaningless to me.
And before the sole and universal retort of "Transphobia" gets trotted out none of this makes any practical difference in how people should be treated. A guy who wants to wear dresses and makeup and have sex with other men and take on zero of the roles traditionally associated with women and avoid roles traditionally associated with men should absolutely be able to do so absent legal restriction, discrimination, judgement or harassment.
Just being told essentially "Treating X and Y exactly the same, you have to see X as Y" is where I get lost. It's not even that I don't want to, I literally can't. You're demanding I recognize a distinction without difference who only criteria is someone else's purely internal conceptualization.