I think it's also partially symptomatic of the general difficulty severe autists like himself have with theory of mind - he struggles to accept the fact that other people are not obligated to conform to the "scripts" he's developed/acquired for them. He thinks he's unlocked some concrete "rule" for human interaction (I identify as woman = society provides asspats), but fails to account in the formula for the autonomy of all of the other actors involved. To the turbo-autist, that's like having a calculator where you input 2 + 2 and it gives you an answer of 47.
Edit to add: in a way, I can't blame him. Looking at some of the utterly unconvincing monstrosities on reddit that get asspats and choruses of validation daily, why wouldn't some gangly teenage SPED be able to convince himself he's a real woman with enough autism? He's as much a "real woman" as any of the other trannies, he's just even less self-aware than they are.