This is quite late, but to me douche implies lack of both self-awareness and self-reflection. "Why am I so intent on insulting this TV show at every available opportunity?" "Why do I have such a strong blanket opinion of political label A?" "Why am I acting like this to someone I barely know?" None of these are questions a douche asks himself.

This lack of curiosity indicates a lack of critical thinking ability and consideration that's almost certain to adversely affect other facets of one's personality. A douche is someone who sets off an alarm bell, "this is a person that will be prone to thoughtlessness." A douche doesn't comprehend why they're a douche, and won't spend much time trying.

I'd say this is probably the reason no one self-applies the term. An asshole often knows he's an asshole, but no one will own up to being a douche, because that's someone who no one wants to be around.