This is, of course, not a question with an objective answer because we cannot know for sure why things like the Progressive Era arise or die out. However, we can speculate that WWI gave rise to the '20s in two ways.
First, Progressivism was a confident philosophy, believing in people's ability to improve themselves and their society. It believed in fairly constant progress in society. WWI helped to damage this confidence. If people could be stupid enough to allow this terrible war to begin and to continue for so long, how could we have confidence in their intelligence and their ability to improve themselves?
Second, WWI gave way to a desire for "normalcy." After the traumas of the war, people wanted to simply have some fun. They were no longer all that interested in earnest attempts to reform society. Instead, they preferred to enjoy the "Jazz Age."