Jay Gatsby is the protagonist of The Great Gatsby by F. Scott Fitzgerald. When we meet him, he has been in love with Daisy Buchanan for five years, though we do not learn that at first. When he met her, Daisy was eighteen and unmarried, and the two of them fell madly in love. He was a young soldier, without many prospects. Daisy, on the other hand, was a rich socialite who grew up with all the comforts and standing of old money.
When Daisy was not allowed by her family to follow Gatsby and tell him goodbye before he shipped out, she has a chance to make a choice: follow the dictates of her family or follow her heart. She chooses the former, money and social class, over love and an uncertain financial and social position. She suffers for a bit, but soon she marries a man who has what she settled for: money and social standing. He has no class and in fact she knows Tom is a womanizer; though she has second thoughts the night before the wedding, apparently still feeling something for Gatsby, she proceeds with the nuptials.
Years later she is reintroduced to Gatsby, and now he is someone whom she might have been able to marry five years ago. Gatsby has spent that time trying to earn and make and be everything Daisy wanted, trying to be worthy of her love. Unfortunately for him, he is the better person in that regard, as he proves at the end of the novel.
The devastating moment you mention in your question happens in chapter seven, and the incident is the catalyst for all the devastating things that follow. Daisy and Gatsby have been conducting an affair which Tom has discovered; he is outraged (ironically, despite the fact that he is in the midst of a violent, low-class affair) and the scene is awful. When Gatsby asks Daisy to say that she never loved Tom, it is not out of any real jealousy but out of his rather romantic nature. He simply wants things now simply to be as if nothing else (including her marriage to Tom) had ever happened.
"Oh, you want too much!" she cried to Gatsby. "I love you now – isn't that enough? I can't help what's past." She began to sob helplessly. "I did love him once – but I loved you too." Gatsby's eyes opened and closed.
"You loved me TOO?" he repeated.
Daisy's response does not kill Gatsby's romantic dream (twice more before the end of the novel we see this unrealistic hope that his dreams of being with Daisy will still be realized), but it is certainly a hard blow for him to bear.
What Gatsby wants is for five years of living to go away (except, of course, for his financial and social improvements) and to just be with Daisy as they both wanted back then. In chapter six, Nick notes:
He wanted nothing less of Daisy than that she should go to Tom and say: "I never loved you." After she had obliterated four years with that sentence they could decide upon the more practical measures to be taken. One of them was that, after she was free, they were to go back to Louisville and be married from her house—just as if it were five years ago.
In one sense it is not too much; in a practical sense, however, it is nothing but a grand illusion, for such a thing is not possible. In short, then, he does want too much because it is something which is impossible for him to have. Nevertheless, Nick, who abhors much of what Gatsby represents, admires Gatsby for this "romantic readiness" and understands Gatsby is "worth the whole damn bunch put together." It is an admirable dream and vision, but it is too much to ask.