The only reasonable explanation for the word asexual being used this way is that people heard it in biology class and didn't have the vocabulary to express what they mean for a different phenomena among humans. Non-sexual (or perhaps 'insexual')seems like a far more appropriate term, as asexual has a more definitive meaning relating to a creature that reproduces without a mate, rather than one who avoids reproductive processes. It's somewhat (though not entirely) similar to the difference between amoral (something that is without morals) and immoral (something that goes against morals).
I suppose fortunately the language does generally maintain the proper idea when speaking about something other than 'identity'. We would typically say, for instance, that two friends have a non-sexual relationship, rather than an asexual relationship (among other differing examples). Asexual is reproductive. Non-sexual is not reproductive.