This is a fascinating question to discuss in response to this story. The issue is that we and the villagers are never actually sure what the arrival of the angel signifies or means. Does it actually represent a transcendent or religious experience? The villagers offer up a whole flotilla of theories concerning the arrival of the angel, and the narrator tantalises us by never providing us with any concrete meaning or conclusions that we can make. If the angel is a celestial visitor, it is clear that the villagers do not treat him as such:
...they found the whole neighbourhood in front of the chicken coop having fun with the angel, without the slightest reverence, tossing him things to eat through the openings in the wire as if he weren't a supernatural creature but a circus animal.
Even the priest of the village, Father Gonzalo, who we expect to be slightly more knowledgeable than his flock, shows his ignorance and petty nature through his assumption that since the angel can't speak Latin he can't actually be an angel. If transcendent or religious experience is there for us to participate in, this story suggests that we often miss it or are blinded to it becuase of our own ignorance, perspectives prejudices. How often are transcendent experiences available to us that we miss because of our own stupidity?