"the exception that proves the rule" is such a terrible expression. I do not understand why people use it.
At some point I thought that it absurd on purpose but I had some people explaining me the rationale behind it (there is no rationale - if there is an exception it at best weakens the "rule")
The expression is referring to an implicit or unstated rule. Defining it is hard but people know when it has been broken. Hooters is an exception, the rule is, don't be like Hooters.
It’s a folkism, but consider this: If a rule doesn’t have any exceptions, is it really a rule? If a rule doesn’t exist how could there be any exceptions?
This phrase only made sense when it was explained to me that it’d be better phrased as “the exception that proves the existence of the rule”.
(if there were no rule, there wouldn’t be any exceptions to it, or nothing would seem exceptional with respect to the (previously unstated) rule)
‘Prove’ was historically used as a synonym for ‘test’, which gives the phrase quite a different meaning. Like how ‘result’ is now sometimes used to mean ‘positive outcome’, as in a football fan saying ‘we got a result’