Sorry to be pedantic, but I think it's implied that the universe of discourse is "all things that are attempting to kill you." The contrapositive under that assumption isn't absurd.

Sorry to be even more pedantic, but even with your correction, the phrase still doesn't make sense. Maybe something that was attempting to kill you but fails makes you weaker, so that the next threat kills you more easily.

If a car runs me over and breaks something in my body, but I manage to survive, it doesn't make me stronger or car-crash resistant.

I'm not defending the original quote--I was just saying that the contrapositive "that which doesn't make you stronger, kills you" seems overly absurd unless you consider the universe of discourse.

What doesn't kill you makes you almost dead.