Comment by AnthonyMouse

The implication is that the exceptions are outliers.

If your rule is that carpenters are usually men and someone goes into a carpentry conference with 1000 carpenters and points out that 50 of them are women, you get to say "exception that proves the rule" and be right.

If your rule is that carpenters are usually women and someone goes into a carpentry conference with 1000 carpenters and points out that 950 of them are men, that's not the exception that proves the rule because 95% of the target population doesn't qualify as an exception.