“A Very Old Man with Enormous Wings” is set in an unnamed coastal town in a Spanish-speaking country where the Catholic Church has a lot of influence. Because Marquez is Colombian, and Colombia contains these elements, scholars generally agree that the story is set there, but Marquez does not make this explicit. The story’s fantastical and folktake-esque elements—such as the existence of angels and spider women—intentionally make the time and place in which the story is set hard to define.
It is possible that Marquez left the setting ambiguous as a way of connecting the events of the story to larger events happening in the world at the time of writing. For example, the everyday cruelty of his characters toward the angel can be seen as paralleling the cruelty of the Conservative Party toward impoverished members of the Liberal Party during La Violencia (the Colombian civil war of the 1940s and 1950s), or even as a symbol of the horrors of the Holocaust in the 1940s.
While the story could be subtly referencing specific historical events, it could also simply be capturing the human pattern of rejecting what is unfamiliar. People anywhere can lack empathy, Marquez hints in the story, and this lack of empathy can lead to all manner of cruelty.