"I find the common definition of asexual as, "someone who doesn't want to have sex with anyone" somewhat problematic, since nothing stops asexuals from wanting and even enjoying sex. " (sorry, I don't know how to use the quote function)
Although sex is not something that I wish to 'do', I have wanted to have it with someone. I wanted it as some hypothetical thing I thought people needed to do to have to 'truly' have a real relationship. I wanted the idea, not the reality of a sexual relationship.
I can see how someone can want actual (not hypothetical) sex without experiencing sexual attraction. I have not yet encountered a situation in which I have felt someone is wrong in how they self identify. I hope this helps somehow. I'm stumbling over these concepts because my range of experience is very limited (I apologize for this ignorance, I'm working on it)