The quote is usually attributed to Friedrich Nietzsche: Was mich nicht umbringt macht mich stärker. In German it reads and sounds more like poetry, which is why it seems probable to me that Nietzsche borrowed it from Goethe, who was writing a century earlier. But does the rhyme suggest a reason? Perhaps it does, or can, in matters of the emotions.
In the brute physical world, and the one encompassed by medicine, there are all too many things that could kill you, don’t kill you, and then leave you considerably weaker. Nietzsche was destined to find this out in the hardest possible way, which makes it additionally perplexing that he chose to include the maxim in his 1889 anthology Twilight of the Idols.
In the remainder of his life, however, Nietzsche seems to have caught an early dose of syphilis, very probably during his first ever sexual encounter, which gave him crushing migraine headaches and attacks of blindness and metastasized into dementia and paralysis. This, while it did not kill him right away, certainly contributed to his death and cannot possibly, in the meanwhile, be said to have made him stronger.
The most he could have meant, I now think, is that he made the most of his few intervals from pain and madness to set down his collections of penetrating aphorism and paradox. This may have given him the euphoric impression that he was triumphing, and making use of the Will to Power.
More of Hitchens’ reflections on death and suffering can be found in his short book on Mortality.