If you've ever taken a class on logic you will have learned about contrapositives. The constrapositive of the statement "A implies B" is "not B implies not A". So, for example, if you have the statement "the presence of rain implies the presence of clouds", the contrapositive of that would be "the absence of clouds implies the absence of rain". What's important about contrapositives is that they're logically equivalent to the original statement. That is, they mean the exact same thing.
The title you see above is commonly cited as the contrapositive of the popular saying "whatever doesn't kill you makes you stronger". But it doesn't seem equivalent, and I'm here to argue that it's not.
Well, kind of. I'm not a crank who's gonna suggest that our model of logic itself is fundamentally mistaken and contrapositives aren't actually equivalent. Rather, I'm going to point out an aspect of the semantics of certain statements that makes their contrapositive imply something different than the original statement.
That aspect is cause and effect. In everyday English when someone uses an if A then B kind of statement what they often mean is that A causes B. In our example, "whatever doesn't kill you makes you stronger" implies that things that don't kill you cause you to become stronger. But when we consider the contrapositive, "whatever doesn't make you stronger kills you", it is implied that something failing to make you stronger will itself cause you to die, which is obviously absurd. While being logically equivalent, there's an implied meaning about cause and effect that gets reversed.
This change in implied meaning happens because the equivalence of contrapositives only exists for logical implications, and not cause and effect relations. That is, while "A implies B" is the same as "not B implies not A", "A causes B" is not the same as "not B causes not A". Implications are not cause and effect relationships; just because differentiability implies continuity, that doesn't mean it causes continuity, and so these complications can arrise when you treat causal statements like implications.