Gatsby claims he was "educated at Oxford", "hurr[ying] the phrase" (pg65) "or swoll[ing] it, or chok[ing] on it" (pg. 65) as if he was telling the untruth. Causing his "whole statement [to fall] to pieces" (pg. 65). Gatsby claims he knew Nick from "the Third Division during the war" (pg. 47). Nick was in the "ninth machine gun battalion" (pg. 47), Gatsby was "in the seventh infantry until June 1918. There were 10–15K case soldiers in each division, Nicks division having 3,772 soldiers and Gatsby's with 707 soldiers.
In chapter three Gatsby gives a hand written invitation to Nick for his
party (pg. 41), something he never does. Then the following day takes Nick out to lunch, introducing him to Wolfsheim (Pg. 69), a shady underground business connect who fixed the World Series in 1919. Gatsby has set up a meeting for miss Baker and Nick in regards to miss baker telling to nick to set up a meeting with Daisy, and him (pg. 67). Afterward, Nick and Gatsby have lunch and are about to leave. Nick happens to see Tom, his cousin Daisy's husband, deciding to introduce Gatsby to Tom. In the midst of Nick introducing them, Gatsby disappears before Nick could even do so. We, later on, find out that Daisy and Gatsby know each other from the past (Pg.86). "it was a strange coincidence", " but it wasn't a coincidence at all " Gatsby bought the house to be just across the bay" says Nick (pg. 78). Which would explain why Gatsby disappeared when he tried to introduce him to Tom, given the fact that "he would never so much as look at a friend's wife" (pg. 72). He did not want to be introduced to Tom.
Gatsby goes out of his way to make sure nick gets a special invite to his party, he takes him out to lunch, and gets to know him, doesn't want to be introduced to Tom. And in reality gets a meeting set up for Daisy and himself. Not possibly knowing Nick from the war, with them being in two completely different divisions. Making his whole intentions and image unbelievable.