Prepositions, ending with--understanding Churchill

As a commenter pointed out, Winston Churchill is often quoted as making this statement about the rule against ending sentences with prepositions:

“This is the type of errant pedantry up with which I will not put.”

Or some other version worded slightly differently. (Note: the original quotation probably used "arrant," meaning utter or notoriously bad, not "errant," meaning wandering off, fallible.)

Churchill's statement is sometimes misunderstood. In fact, I've seen it quoted as support in favor of the rule against sentence-ending prepositions on a few occasions--once by a lawyer in the Texas Bar Journal.

But Churchill was being ironic:

When Winston Churchill was chastised for ending a sentence with a preposition, he wittily responded. “This is the type of arrant pedantry up with which I will not put.” Churchill’s retort illustrates that attempts to avoid ending a sentence with a preposition can be labored and ludicrous.

David Angell & Brent Heslop, The Elements of E-mail Style 79–80 (Addison Wesley 1994).

You see, the more natural-sounding sentence, which Churchill preferred, would have been:

"This is the type of arrant pedantry I will not put up with."

But in an ironic jab at his tormenter, he avoided the sentence-ending preposition with what, I hope you'll agree, is a stilted and silly construction.