The biggest contradiction within Jay Gatsby's character is that he proved himself capable of extraordinary success, but became bogged down in yearning for Daisy, a woman who married another man soon after she promised herself to him.
Nick says Gatsby's overwhelming characteristic is "an extraordinary gift for hope, a romantic readiness such as I have never found in another person..." This gift for hope, which is prompted by his desire to make himself worthy for Daisy, led him to gain enough money and status that he was able to purchase "a factual imitation of some Hotel de Ville in Normandy" with "more than forty acres of lawn and garden." His house was opposite Daisy's on Long Island Sound and did not lack in grandeur.
This is something quite extraordinary for a man who came from parents who "were shiftless and unsuccessful farm people." As a boy, Gatsby created a brutal schedule for himself in order to make himself successful. Gatsby's father, Mr. Gatz, said, "Jimmy was bound to get ahead. He always had some resolves like this or something."
However, this extraordinary success is contradicted by Gatsby's inability to let go of his past with Daisy. Nick says Gatsby "wanted to recover something, some idea of himself perhaps, that had gone into loving Daisy." In addition, Nick says that Gatsby's life was "confused and disordered" since their months together. This desire to return to a time when Gatsby was with Daisy is what prompts Jay to cry, "Can't repeat the past? Why of course you can!"
Unfortunately for Gatsby, this desire to repeat the past is what leads to his ultimate demise. His relationship with Daisy causes Tom to look into Gatsby's past. And his desire to protect Daisy is what leads George to believe it was Gatsby who killed Myrtle.
Therefore, Gatsby's extraordinary gift for hope and ability to strive forward in his life in contradicted by his inability to move away from his past with Daisy.