In The Great Gatsby, why does Gatsby say “old sport”?

Gatsby uses the phrase "old sport"  to sound upperclass British, more like the "Oxford man" he claims to be. It's an English phrase, similar to "I say" or "I say, old chap," and it grates on the ears of Tom Buchanan, who is not for a moment fooled that Gatsby is anything but an upstart: "'Oxford man!" [Tom says]  "'Like hell he is! He wears a pink suit.'"
Tom shows his irritation when he says to Gatsby: "All this 'old sport' business. Where did you pick that up?" Later he snaps "Don't you call me 'old sport'!"
Despite Tom's irritation, this a characteristic phrase that Gatsby uses all the time, to everyone he wants to ingratiate himself with: Nick, Tom, the policeman who pulls him over, guests at his parties. Nick understands it as way for Gatsby to feign intimacy without actually being intimate at all: "The familiar expression held no more familiarity than the hand which reassuring brushed my shoulder," Nick says. 
This phrase is part of Gatsby's incongruity or mystery, another part, like the uncut books in his library or his claims of big game hunting in Europe, that just doesn't quite add up. In the hands of less sympathetic writer than Nick, it could come across as just part of a con, but Nick sees Gatsby, the tragic dreamer, as greater than that.