I think (we) Americans hate failure only when people give up.
We have a very long tradition of failure leading to success, everything from Edison trying hundreds of lightbulbs to Don Draper in Mad Men reinventing himself after failure.
Our bankruptcy laws are different from other countries in how lenient they are towards the debtor. And, of course, the entire culture of Silicon Valley is about failure after failure followed by success.
And it's not even conventional, economic success that we want. We're happy when someone finds happiness even if not financial success. The rich-person-gives-up-everything-for-love is a familiar American trope.
We don't like failure, but we forgive it, as long as we keep trying.