Even if you strip out all the supernatural woo-woo, "A Very Old Man with Enormous Wings" sends a pretty clear message: be nice to old people. Even though the angel is an amazing, fantastic being, with wings—wings!—and probably lots of cool stories to tell, no one cares. Once the reality of his baldness and toothlessness sets in, he's just a burden. In fact, Elisenda doesn't even appreciate him until he's gone. We might even go so far as to say that his wings could represent the incredible gift of surviving to old age—and the way that it can be more of a burden than a blessing. Grandpa Simpson can relate.
The way the townspeople treat the old man is a reflection on our society's cruelty toward the elderly.
The old man frightens the townspeople because he reminds them of their own mortality.