Tom Buchanan represents the American Dream by revealing the American Dream as a myth. The American Dream is often understood in terms of Horatio Alger's "rags-to-riches" stories wherein an impoverished protagonist (such as in Ragged Dick) is able to "pull himself up by the bootstraps." Buchanan, however, has never experienced a life of poverty and does very little in the way of hard work. Instead, Buchanan represents arguably the worst aspects of American wealth. He is born into wealth, exhibits white supremacist beliefs (as evidenced by his reference to Lothrop Stoddard's The Rising Tide of Color as well as his treatment of blacks in Manhattan), and exhibits very little in the way of the work ethic that is often associated with the American Dream.
At one time, someone like Buchanan would have been considered admirable due to his aristocratic background as well as his success as a football star at Yale. As scholar Christian Messenger has pointed out, Tom Buchanan represents "the demise of the Ivy League athletic hero." Messenger further notes that this representation is, in actuality, "the story of an American loss of innocence and a decline in a belief in social privilege and an ideal of responsibility."
For Fitzgerald, Buchanan is an alcoholic bully who feels entitled to a life he does not deserve. After having experienced success in college and having been spoiled by his upbringing, it is very likely that Buchanan is unable to cope with the failure of his marriage and the threat of Gatsby, whose new wealth is (at least on the surface) a more genuine version of the American dream than Buchanan's. As a result, Buchanan spends his days berating his wife, ignoring his daughter, and committing adultery with a woman from a lower social class whom he can manipulate through his wealth.