Also, in Chapter 7, Tom accuses Gatsby of never having attended Oxford, at which point Gatsby reveals that he did, in fact, attend Oxford -- but only for a few months:

[...] I only stayed five months [...] [i]t was an opportunity they gave to some of the officers after the Armistice [...] [w]e could go to any of the universities in England or France (The Great Gatsby, ebooks edition, Chapter 7).

Of course, Gatsby knows that calling himself an "Oxford man" helps to increase both his reputation and his chances of winning Daisy, so he uses those few months to his advantage.  It is Jordan Baker, however, who points out at the beginning of the novel that she does not believe him when he says he's an Oxford man, and then again with Nick Carraway when Gatsby rushes through the phrase "educated at Oxford" (Chapter 4). 

In his search for the American Dream, Jay Gatz severs his relationship with his parents by rejecting his surname and recreating himself as Jay Gatsby, whose impressive resume includes having graduated from the prestigious British university, Oxford. Most prestigious, this university is recognized as one to the top institutions of higher learning in the world.

By claiming to have gone to Oxford, Gatsby places himself among the elite of the world, giving himself an aura of the cosmopolitan and as well as one of the intelligentia. Clearly, Jay Gatsby assumes a role in order to draw attention to himself so that his neighbor Daisy Buchanan will be impressed with him and turn her interest upon Gatsby so that he can reclaim Daisy and renew his relationship with her after several years. 

The truth was that Gatsby of West Egg, Long Island, sprang from his Platonic conception of himself.

These words of Nick Carraway, the narrator, characterize Gatsby whose sole raison d'etre is to attain the materialistic Daisy Buchanan.