Ever wonder if just doesn't understand gender at all to any degree? He doesn't understand JERKS, can't live up to the masculine expectations of men and due to autism can't relate to them. He doesn't understand women, nor the discrimination many women face in society, and again due to autism only feels like he can relate to women because he shares more feminine traits with them than males which is further skewed by the media he views. Thusly, in his mind, he must be a woman born in a man's body, hence the gender dysphoria. I know this has all been said already but it's hard to impress what I'm getting at. He's straight and like a lot of straight men don't like looking at other's ducks. His hatred of his own duck could be due to it's deformation, and a reminder that he belongs to a gender he loathed for a long time. He's obsessed with gender, without having any idea about the nature of either.
He finds lesbians hawt, and again his twisted logic interprets this as his being a woman in mind and soul. I guess what I'm trying to say, as best I can, is he's like a personification of gender neutrality. I feel like he'd be happier and far less obsessive about it if he was born without a duck or china.