How does The Great Gatsby challenge the established values of its time?

It's normal in cultural historiography to state that the 1920's were a time of vast change in American life. Long-established ideas were stood on their heads, and older ways of thinking were systematically debunked. The decade was very much a precursor of what was to happen 40 years later, in the 1960s.
In The Great Gatsby, the title character is an upstart, a man of humble, uncertain background who has established himself as a plutocrat, one whose power is based chiefly on wealth. Though America was rooted in egalitarian ideals, most power in this country initially stemmed from inherited wealth, as in Europe. The great exception had been Abraham Lincoln, a man of working-class background and little formal education who became the greatest president in US history—perhaps precisely because only an outsider could understand the false and dysfunctional dynamic of the nation and have the boldness to do something to change it. Gatsby is no Lincoln, but he is a "self-made" man, and the fact that he can achieve power and prestige is a challenge to the established social hierarchy of not only the US, but of the world overall of that time.
The people who attend his parties are similarly part of this meritocracy in which status in society has begun to be based on new wealth. At one of Gatsby's parties, the orchestra plays a piece called "The Jazz History of the World." In the America of this period, jazz, to the establishment, represented something both ravishing and still, in a way, slightly disreputable. Nick comments that the nature of the piece eluded him somewhat. But more than anything else it is a musical analogue to the overturning of social norms that Gatsby himself represents. The elitism of the nouveau-riche who come together at the party is a foreshadowing of the dynamic that has come to dominate the US over the past hundred years. Throughout Fitzgerald's novel, there is a consciousness of this new meaning of wealth for its own sake, and at the same time a questioning of its validity. In the end, Gatsby himself, though flawed, is a positive symbol, as the famous closing statement about his belief in "the green light," in an "orgiastic future," spells out so poetically.