The eponymous "very old man" is a symbol of the flawed manner in which, throughout the centuries, organized religion has forced an imaged of what should be considered "holy".
The combination of the villagers' ignorance, their lack of worldly sophistication, and their religious rote-learning leads them to conclude that this strange visitor is an angel. However, since he is unkempt, disheveled and completely dissonant from the cherubs universally acknowledged by church-goers everywhere, the villagers make a freak-show out of him. They do not appreciate the salient nature of the wings. They do not acknowledge the petty miracles that this strange being has granted. They do not even commiserate with him for his current state. Even the small miracles that this creature grants are dismissed because they are not big enough miracles. The looks of the stranger are what ultimate drive the villager's choice of ignoring it. They merely stare, try to feed "it", and quickly dismiss him when a new freak of nature appears in town at the country fair.
Using this unlikely heavenly envoy as a conduit, Garcia Marquez conveys a clear message regarding the state of human spirituality: organized religion, and not our own search for spiritual knowledge, has delineated what is and what is not to be considered worthy of veneration. Even when the very old man catches flight and goes away, he is seen as a "distant point in the sky" that makes absolutely no difference to Pelayo or Elisenda; after all, they have found benefit in this man by profiting from him. Hence, the creature that could have been used to make a difference clashed against a flawed human condition that could not see past their blindsided eyes.