Teacher here. It is a misreading of one word. "Prove" used to mean "test", not "confirm": same root as probe, a proving ground, proofing armor. So "the exception proves the rule" means the exception TESTS it. A rule put to a hard case comes out stronger if it holds.
There is a legal origin too: exceptio probat regulam. The exception marks the case the rule was never meant to cover, which is how you see where the rule actually applies.
What it is NOT: an exception as evidence for the rule. Left unexplained, an exception weakens a rule. Named and placed outside its scope, it sharpens it. Direction matters.
Tell me the rule you were testing and I will tell you which one you have.
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