Looking at Gatsby after having read the novel we will have encountered Nick Carraway's passionate but enigmatic statement about his wealthy, bootlegger neighbor.
Nick...tells him he is better than the “whole rotten bunch put together.”
Nick says this after finding that Gatsby is waiting for a phone call from Daisy, after all that has happened and any normal person would have given up hope. Gatsby does not give up hope. His life is founded on it.
Gatsby...loses a sense of reality but...believes in “a promise that the rock of the world was founded securely on a fairy's wing.”
Hope, self-belief, and confidence in the brightness of the future constitute a special kind of innocence in Jay Gatsby. This combination of qualities, given the nature of his life, must be seen as remarkable. At least, Nick sees these qualities as remarkable.
In this poignant innocence Gatsby is truly great. His sensitivity to the promises of life, as Nick says, is heightened. The man is a poet of hope, as it were, willing to go on and on in pursuit of a dream, fully believing in it, unwavering, assured, despite all obstacles.
In a social context of crass materialism, Gatsby anchors his hopes to a girl - not even the Daisy he meets, but to her former self, the girl from his memory. This choice sets Gatsby apart as well. He is exceptional because he is a dreamer who dreams of romantic love in a time of broken marriages and value-less material elitism.
What makes this romantic dream in Gatsby all the more remarkable is that he has to break up a marriage to achieve it. He also has had to become a criminal to approach the dream.
Only a person with a great sense of hope and innocence could maintain such a firm vision of romance in the face of these circumstances. This is the how and the why of Gatsby's greatness.
The title of the novel, it should be said, is intended to be ironic also. Gatsby's greatness is a greatness despite of his achievements, not because of them. His persona is a fraud. All the good things about him were intact before his rise to wealth and power.
This is part of the thrust of the novel's satire.