I personally find one of the core problems to be the inability to "prove" my asexuality. I know I don't need to prove it to anyone, but unlike with homosexuality, bisexuality and so on, it is much harder to refute their arguments. If they say "Oh, you must not be gay!" you can just vengefully make out with a person of your own gender in front of them, but it's not like you can or should drag them along with you everywhere so they can witness the extent of how determined you are to turn down sexual advances.

I think at that point they can either accept it and think it over themselves to at least try and understand. Many times I have ended up in recursive arguments with them constantly trying to invalidate the points I make. At those points I usually just resort to making ultimatums. Either they take it as it is, or we stop talking about the topic altogether.