In The Great Gatsby, Nick is primed not to believe in what Gatsby says because of the aura of mystery—which Nick believes might be a little "sinister"—that swirls around him. At the first party of Gatsby's parties that Nick attends, he hears wild rumors about Gatsby as criminal, spy, or murderer. The source of his vast wealth is unknown.
Further, his own probings of Gatsby bring up lies. For example, in the following exchange, Gatsby exposes himself. After Gatsby says "by God's truth" that he is from a wealthy midwestern family, Nick asks,
“What part of the Middle West?” [...]
“San Francisco.” [Gatsby says]
As the conversation goes on, Gatsby tells more lies:
I lived like a young rajah in all the capitals of Europe—Paris, Venice, Rome—collecting jewels, chiefly rubies, hunting big game, painting a little, things for myself only, and trying to forget something very sad that had happened to me long ago.”
With an effort I managed to restrain my incredulous laughter. The very phrases were worn so threadbare that they evoked no image except that of a turbaned “character” leaking sawdust at every pore as he pursued a tiger through the Bois de Boulogne.
The above is a telling passage. As Nick's desire to laugh indicates, as well as his image of Gatsby chasing a tiger through a Paris park, nobody big game hunts in the capitol cities of Europe. As Nick realizes, Gatsby has fashioned his own identity based on romantic stories he has heard or seen in movies.
Gatsby's stories don't add up, but like a good con artist, there are enough elements of truth in what he says that he can't be entirely dismissed. He was in Europe during the war, for example, and did spend some time, as he claims, at Oxford.
Despite Gatsby's untruths, Nick is nevertheless seduced by Gatsby's charm and the audacity of his self creation. And as Nick shows in the novel, none of the major characters are entirely truthful.