Ah, to psychoanalyse, or to medicalise...that is the question.
One could do either or even both, seeing as labels are political but also presumably reflective of something else. Here's two examples:
1) A friend of mine called himself asexual because of a reaction to a crisis of sexual identity. I myself, in my latter stages of school, took up the asexual banner as a stand against what I saw to be the stifling heternormative construct that tended to dominate school social dynamics. At the time I said "well I don't appear to have homosexual inclinations" and also "I don't have any interest in this sleazy world of picking up chicks etc." so I said "fine, I'm asexual."
I would, however, note that in many cases (mine included) the 'asexual' label can often be a way of hiding skeletons in the closet.
2) The partner of another friend of mine had a stroke which precipitated alcoholic dementia, after which (as can commonly be the case for this kind of presentation), they completely lost the conception of 'sex' and the ability to be aroused. This would, I suppose, in a medical sense make them 'asexual' but seeing as they were in a same-sex relationship this would differ from the identity-politic domain of previous...perhaps that person considered themselves still homosexual due to their relationship. I wasn't clear on that detail as it didn't appear particularly relevant.
One has to remember that any discussion pertaining to 'sexuality' and various orientations, predilections and 'alternatives' fall under the current rhetoric (which I hold to be unwieldy), and thus confound a whole bunch of domains. We had difficulty making any semblance of a definition of homosexuality. Hell, I bet the same would apply to heterosexuality. And given that the reported sample space is so small here, it'd be even harder to define 'asexuality'.
Also, by psychiatric definition (DSM-IV TR recommendations...which I support in this case), something isn't a pathology unless it causes much distress or maladaptive functioning. From above, the former wasn't pathological (assuming that could even be called 'asexual')...the latter most certainly was. More for the partner of said dementia patient.
Speaking of which, personally I wonder what would happen if we ran a series on the 'paraphilias'.