Tom Buchanan prevents Jay Gatsby from living happily ever after, both in Gatsby's head (for much of the story) and then literally (by denying him Daisy and then taking actions that lead to Gatsby's death). Nick introduces Tom Buchanan as an excellent sportsman, but that's about the only thing he has going for him. He's wealthy, restless, and "cruel"--not a good combination (1).
But if you like your antagonists cut out in clear black-and-white, Tom isn't the guy for you. Just when we feel safe about sticking Tom in the villain box and sealing the lid shut, we start to (gasp) feel sympathy for him. At the Plaza, for the first time we see a sensitive side to Tom. Or, as Nick says it, the man displays "a husky tenderness" towards his wife (7). He declares he loves her, that he's always loved her, mentions some tear-jerking scenes between them, and declares he's going to treat her better from now on.
By the end of the novel, even Nick is coming around. He declares that he can't forgive Tom for what he's done, but that he certainly understands that, in Tom's mind, all his actions were "entirely justified" (9.144). So there you have it: Tom Buchanan, the not-so-evil bad guy.
If you're feeling fancy, you could say that Gatsby's antagonist is his dream of being with Daisy. This fantasy has driven his actions, propelled him forward, and, ultimately, clouded his judgment all the way to his death. And that sounds pretty antagonistic to us.