"A Very Old Man with Enormous Wings" plays heavily on ambiguity.

Garcia Marquez never allows the reader to settle comfortably into one attitude or the other...

For this reason, identifying a single meaning in the winged character is quite difficult. A number of symbolic meanings are available depending on our interpretation. 

The most compelling reading of this character sees him as a representative of people's faith, both in humanity and religion. Like religion in the context of the story, the man is open to interpretation. Also, religion in the text is represented wholly by humans and functions as an optional moral guide, to be chosen or cast away according to whim. 

...the villagers' magical beliefs are in fact ridiculous delusions; but at other times, the reader seems expected to take logically impossible events at face value.

Though the man is seen initially by some as an angel, he disappoints the set ideas that people have about angels. He is far from majestic.  He is instead more like ''a senile vulture'' or a ''decrepit hen.''

Instead of presenting a majestic, awe-inspiring figure, Garcia Marquez describes a creature with mortal weaknesses and senility...

The man is treated like an animal because he is seen as an animal. We can take this as a comment on the villagers views of humanity. As the man has failed to meet their expectations, the man is relagated to a coop, ridiculed and debased.

He is, then, a projection. He is what the people believe him to be. He is an avatar of perspective and belief. To go futher than this in our interpretation is to undermine the power of the ambiguity at the heart of the story.

The man is and isn't an angel. He is and isn't "just a man".