The Exception Proves The Rule?

I'm certain that you've heard the phrase "the exception proves the rule" dozens or even scores of times during your lifetime. And each time you heard it, assuming that you received an American public education somewhere besides California or Arkansas, you were troubled by a little voice whispering, "that doesn't make any sense". Don't worry. That little voice is what's left of your I.Q. and it's your ticket to being categorized as intellectually salvageable during the coming purges. The truth it that, as used in America, this aphorism doesn't make any sense. It is, in my experience, always used by self-important blowhards (or those seeking to be self-important blowhards) when their opinions-stated-as-facts are challenged by actual facts that counter their contentions. A common example is "all birds can fly". If you follow modern American usage logic the existence of penguins would prove that rule to be true, when it does just the opposite.
So, what does it mean? It is derived from the Latin Exceptio Probat Regulam. Probat, or prove, in this case is defined as test. As in a proving ground. Anybody who came of age in the 60's and 70's remembers rocket cars attempting to break the land speed record at The Bonneville Salt Flats Proving (Testing) Grounds. Therefore the statement means that exceptions test the rule or rules, not confirm their validity. Learn well and learn fast. Public means testing is coming and this will be one of the questions. You want another one? Alright. Would've is not a contraction for would of. I know when you say them they sound the same, but one is a shortened version of "would have" and the other has no meaning at all. I've been told that people who miss that one go straight to the gulag (or the rendering plant, depending on whether there is a shortage of glue or dog food at the time). Good night America and good luck!

PS There is another accepted meaning of the above mentioned phrase. That an exception proves the existence of a rule. If parking is free after 6 PM(exception) it hints that there is a rule that prior to that parking is not free (rule). But we haven't devolved to the point where evidence that repudiates a claim also confirms it's validity. Not yet, anyway.