Nietzsche was wrong. He was wrong about quite a lot, but he managed to write in a manner that gets people believing he is right, even when they know he is wrong. A great example of this is his idea that what does not kill you makes you stronger. Many people believe it when they read it, even though they all know that it is false, because what doesn't kill you can leave you crippled and maimed. Everyone knows that what does not kill you can leave you crippled and maimed, which is weaker, not stronger. Everyone knows he is wrong. And yet, there is something in how he says it that gets people to believe him anyway.
"A wise man ... proportions his belief to the evidence."
— David Hume, An Enquiry Concerning Human Understanding, Section X, Part I.