The very old man with enormous wings...

The man with wings is just a man. Many people are born with afflictions or 'blessings' that are never viewed as being something religious or monumental. They're simply people who are different from the rest. He acted like a old man, he looked like a old man, and some perceived him to be a old man. By my logic he was a old man, who happened to have wings. Some kids are born with eight limbs, like the child in India, but she isn't a goddess, she's just a child.

This affects the story because it shows how people deal with faith, and what they choose to invest in. No one in the story paid attention to the familiar outlets of faith like the preacher, no one paid attention to the letters from the pope. "The most unfortunate invalids on earth came in search of health: a poor woman who since childhood had been counting her heartbeats and had run out of numbers; a Portuguese man who couldn't sleep because the noise of the stars disturbed him; a sleep walker who got up at night to undo the things he had done while awake; and many others with less serious ailments." These people brought their faith to something unknown with hopes of getting the answer. People need hope, and the man is a symbol of how far people will go to get that comfort from faith that they need.