One possible interpretation of the story is that mankind's connection with a spiritual world or a spiritual meaning to life has disappeared. The angel is old and dirty, without human mannerisms and seemingly without higher intellect. It comes across as a circus freak instead of a supernatural being on a higher level than man; most people treat it as a lower being.
...the hens pecked at him, searching for the stellar parasites that proliferated in his wings, and the cripples pulled out feathers to touch their defective parts with, and even the most merciful threw stones at him, trying to get him to rise so they could see him standing.
(Márquez, "A Very Old Man with Enormous Wings," salvoblue.homestead.com)
The message in this interpretation seems to be that without spiritual meaning, people turn exclusively to their own self-interest. The angel might be a messenger, or it might be an unfortunate Earth creature like the spider-woman or the man who can't sleep because he can hear the stars. In either case, the people of the town ignore any possible spiritual message that the arrival of this angel might herald, and act only in their own self-interest, finally ignoring the angel when something more interesting comes along.