The essential plot of The Great Gatsby is very basic and simple. Two men are fighting over one woman. The man who initiates the conflict is Gatsby. He is the protagonist. Without him there wouldn't be any conflict or any story. The other man has to be Daisy's husband Tom Buchanan. He is the antagonist. Gatsby manages to have a love affair with Daisy practically under her husband's nose. The conflict really doesn't break out into the open until Chapter VII when Tom asks:

"What kind of a row are you trying to cause in my house anyhow?"

Daisy is the "bone of contention" or "MacGuffin" in this conflict. She feels herself being pulled in two different directions. She tries to intervene:

"He isn't causing a row," Daisy looked desperately from one to the other. "You're causing a row. Please have a little self-control."

"Self-control!" repeated Tom incredulously. "I suppose the latest thing is to sit back and let Mr. Nobody from Nowhere make love to your wife."

In the end it is the antagonist, Tom, who wins the struggle. He has several advantages over Gatsby. Tom, after all, is already married to Daisy. Tom represents "old money." He has also found out a lot about Gatsby's criminal activities and gangster associates. Daisy is a weak character. She stays with her husband and her little daughter even though she no longer loves Tom and does love Gatsby. 

A rather weak point in the plot is Tom's consenting to let Daisy and Gatsby drive back to Long Island together in Gatsby's big roadster. But F. Scott Fitzgerald evidently wanted the story to end with Gatsby's death. His death, like the death of Anna Karenina in Tolstoy's novel, makes the story a tragedy and closes the novel with finality. Gatsby is totally defeated. Otherwise, he would have gone on loving Daisy and probably trying to win her away from her husband.

The novel The Great Gatsby is a classic tale set in the 1920's. The protagonist is the title character in the story, Jay Gatsby. The antagonist could be argued in this story, because the character of Jay Gatsby is so complex. One could argue that the antagonist is Gatsby's romanticism. He believes that he can turn back time and go back and fix the relationship with Daisy. He had, as Nick explains, "an extraordinary gift for hope, a romantic readiness such as I have never found in any other person and which it is not likely I shall ever find again." However, the most obvious answer to this question is Tom. Tom Buchanan prevents Gatsby from getting what he desires, Daisy. This happens by way of him marrying Daisy, then later in the novel, slandering Gatsby's reputation to Daisy. Finally he takes actions leading to Gatsby's death, using George as his tool. Tom is very muscular and athletic and rich, but he "drifted here and there unrestfully wherever people played polo and were rich together." Nick feels that Tom "would drift on forever seeking, a little wistfully, for the dramatic turbulence of some irrecoverable football game."