Among Fitzgerald's favorite subjects, and those to which he devotes the most time and thought in his novels, are social class, money, and the relationship between the two. In critical works on The Great Gatsby, a distinction is always made between the old money of East Egg, represented by the Buchanans, and the new money of West Egg, represented by Gatsby. This clearly is an important divide, but it is far from being the whole story. In the first place, the old money does not have to be very old, while the new money is very new indeed. We do not know how long Tom Buchanan's family has been wealthy, but we do know that Gatsby was born poor and made his money himself. If someone like Gatsby were to have a son and send him to prep school, then to Yale, the son would fit perfectly well into the Buchanan set. Gatsby's mistake is to try to change his social class in his own lifetime by inventing a fictional past of exactly the conspicuous opulence that would appeal to the newly rich. Due to his conspicuousness, he is detected as an obvious fraud by the real elite.
Nick Carraway is often taken as a spokesman for Fitzgerald himself, and he is in exactly the social position into which Fitzgerald was born. Socially, he belongs in East Egg, but he cannot afford to live there so he lives in West Egg, in Gatsby's shadow. Nick attended Yale with Tom Buchanan, and his money is also old, but there is much less of it. He is therefore in the same social class as the Buchanans, but near to the bottom of it, while they are close to the top. Gatsby is not in the same class at all, despite his wealth.
The class distinction here is historical but is much less rigid and monolithic than the class divide in European countries. There are members of the Boston Brahmin class, both real and fictional, who trace their ancestry back to the Mayflower, who would certainly consider Tom Buchanan a parvenu, along with all the aristocracy of the Midwest, including Fitzgerald himself.