Several of my characters are asexual.... Each for their own reason.
My fursona, of course, as he's exactly me, and I'm asexual and aromantic. Same for my pokésona.
Alastyn just has no sexual drive at all, for no specific reason. He's also aromantic. His only loves are his dad and his brother.
Being from an overly religious family, Amadeus think that masturbation and having sex before mariage are sins, then he wouldn't do it. Also, he's actually gay, but would not admit nor accept it, then would never have sex with a man (as that's a sin too to his religion) nor even have a sexual attraction to one, but he would not have sex with a woman neither as he's not attracted to them. Thus he has no sex, no sexual attraction. However, he has a strong romantic drive, that he's trying to restrain.
Anok, Diey, Galico, Osiu, are asexual because they have no genitals. Can your brain perform a sexual attraction if you never had any sexual organ? I don't think so.
Cherinee had a sexual attraction to only one person on Earth. He never looked at anyone else. But well, now that his wife is dead, of course he's not attracted to her anymore. Then he's not attracted to anyone at all anymore.
Kaoru has no idea of his romantic and sexual orientations, but I'd call him asexual. He's not interested into sex at all. He somewhat feels disgusted by the single idea of touching someone's vagina or dick. But he might be okay being in a relationship.
Maeda and Shiro have no interest for sex nor relationships, but they may in a few years.
Vassili has no sex drive neither, and he wouldn't have anyone to be attracted too anyway, as he's the only one of his species. Also he has no formed genitals...
Well, that makes a lot of asexual characters, actually. But I have some overly sexual ones to balance :D