The exception that proves the rule
The true meaning of “the exception that proves the rule” comes from Cicero’s legal maxim exceptio probat regulam in casibus non exceptis — the exception proves the rule in cases not excepted. If a sign says “no parking on Tuesdays,” the exception (Tuesday) proves that parking is allowed the other six days. The exception doesn’t validate the rule by being unusual; it demonstrates the rule’s existence by being explicitly carved out.
Stephen Jay Gould explains this in his essay “Death Before Birth, or a Mite’s Nunc Dimittis,” collected in The Panda’s Thumb (1980) (Wikipedia). He uses Fisher’s principle of sex ratios: in most species, a 1:1 ratio is evolutionarily stable because any bias creates an advantage for the minority sex. But one mite species has an extremely female-biased ratio — an apparent counterexample. Far from refuting Fisher, though, the mite’s peculiar mating system (brothers mating with sisters inside the mother’s body) changes the evolutionary calculus so that Fisher’s model predicts the skewed ratio. The exception doesn’t break the rule — it confirms it, in exactly the Ciceronian sense: the special case proves the general principle.
Gould’s essay “Death Before Birth, or a Mite’s Nunc Dimittis,” collected in The Panda’s Thumb.
