I can't find anything in the image that makes the claim that asexuality isn't real. I think it's just making fun out of the fact that people make their lack of attraction to anyone their defining characteristic and constantly talk about how 'oppressed' they are.

Asexuals, of course, have their problems they have to go through for their orientation, but I don't necessarily think they line up with that of LGB's, nor do they face as much oppression, at least in my opinion.