You could write a thesis statement which argues that the pursuit of the American Dream is a fool's errand when it is based on external notions of success. In Dexter Green's case, he believes that if he is as wealthy and prominent as the patrons of the Sherry Island Golf...
Course where he caddies—notably, as wealthy and prominent as Mortimer Jones—then he will be happy. His pursuit of Judy Jones, Mortimer's daughter, is largely motivated by his class ambitions. Notice how, in the story, Judy is often described as golden. At one point in the story, she is wearing gold. She is an object that Dexter covets in his effort to be a member of the nation's elite.
His ambition leads him to attend an Ivy League school on the East Coast, despite having been accepted to a business program at the University of Minnesota. He moves to New York for the same reason. When his business associate, Devlin, informs him of Judy's life in Detroit, Dexter is seized with a desire to go to Detroit and rescue her, then realizes that it would be for naught.
When Dexter watches the sun set from his office, Fitzgerald again references the pink and gold colors that have been used to describe Judy and the summer skies in Minnesota during Dexter's youth. While the sun sets, Dexter realizes that his winter dreams have "evaporated" and that the gates of the country club are forever closed. He can never return physically or in his memory. Throughout the story, Dexter has returned home and resumed his relationship with Judy multiple times, just as he has always returned to his "winter dreams" of summers at the golf course. In his office, when he realizes that he can never go back, he feels that he has lost something, but he does not know what it is and cannot bring himself to care.
What is ironic about this ending is that Dexter has achieved the class status he always wanted. However, without Judy, he never quite felt like a success. She, in his mind, was the prize that he coveted, but could never win—proof of his prestige. Fitzgerald often used upper-class women as emblems of success, desired by ambitious young men from lower-class backgrounds in his stories and novels. He uses this theme most notably in The Great Gatsbyin regard to Gatsby's love for Daisy Buchanan.