Why do we say "Pigs Might Fly"?

Meaning:

A sarcastic remark used to indicate that an event is very unlikely and/or to question the credulity of someone. For example, "he said that he'd tidy his room today," to which somebody might reply "... and pigs might fly" or other variations such as "when pigs fly" and "oh look, I think I saw a flying pig."

Background:

According to America's Popular Proverbs and Sayings by Gregory Titelman, the expression "if a pig had wings, it could fly" traces back to Proverbs of Scotland (1862).

But other sources, most notably the usually reliable phrases.org.uk, find much earlier references - the earliest being John Withals' English-Latin dictionary, A Shorte Dictionarie for Yonge Begynners (1616): "Pigs fly in the ayre with their tayles forward."

In Gnomologia (1732) Thomas Fuller moved the expression closer to its modern day form: "That is as likely as to see an Hog fly."

The first known example of the expression in its modern form is from The Autobiography of Jack Ketch By Charles Whitehead (1835): Yes, pigs may fly, but they're very unlikely birds.

In Alice's Adventures in Wonderland (1865), flying swine make two memorable appearances:

"The time has come," the Walrus said,
"To talk of many things:
Of shoes--and ships--and sealing-wax--
Of cabbages--and kings--
And why the sea is boiling hot--
And whether pigs have wings."

and:

"I've a right to think," said Alice sharply... "Just about as much right," said the Duchess, "as pigs have to fly."

Even without evidence of use from the 17th and 18th centuries, the fact that Lewis Carroll included references to flying pigs in Alice's adventures implies that the expression was in popular use at the time.

And now for an aside on the title of Thomas Fuller's 1732 book, Gnomologia. While some might conclude that gnomology must be the study of friendly faced garden ornaments often seen with fishing rods, it is actually a word coined in the 16th century to describe a collection of proverbs (gnome having its roots in the Greek word to know, and logia in the Greek for collection.) The use of gnome to describe diminutive mythological creatures came later, in the early 18th century. And a century or so later, in the 1840s, the first ceramic garden gnomes made their appearance in German gardens.

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