An argument can be made that the environment is the protagonist in Bradbury's "A Sound of Thunder," and Eckels is the antagonist.
Eckels is the antagonist because his action of crushing the butterfly interferes with the delicate balance of the non-technological world of nature. This arrangement of protagonist/antagonist fits with the narratives of Ray Bradbury, who felt that technology threatened the natural order of things.
That Eckels is a somewhat "difficult" person is apparent early in the narrative of Bradbury's short story. For instance, he asks the official at the desk, "Does this safari guarantee that I come back alive?" And, when the clerk tells him that if anything happens to him, the company is not responsible, Eckels angrily counters, "Trying to scare me?" Later, when the time machine takes them to pre-historic times so that Eckels can shoot a Tyrannosaurus Rex, he is told not to shoot any animal that the guides do not okay, nor to step off the anti-gravity path. "Why?" asks Eckels defiantly.
So, the guides try to explain that they do not belong in this pre-historic environment, and they cannot upset the balance of nature:
"With a stamp of your foot, you annihilate first one then a dozen, then a thousand, a million, a billion possible mice!"
"So they're dead," said Eckels, "So what?"
Eckels remains antagonistic even after he steps on the butterfly and alters the world. When he returns to TIME SAFARI,INC. and it now reads TYME SEFARI INC., and he learns of other changes, Eckels remains disputatious as he is accused of violating his contract with the company. When his attitude does not succeed, he pleads that the time machine return and right his mistake, still not accepting that he has caused the drastic alteration of the present because of his non-compliant behavior. Clearly, then, Eckels is the antagonist in "A Sound of Thunder" and nature the protagonist.
The protagonist for most of the story is Eckels. The story itself is focused on his introduction to the idea of going back in time to hunt dinosaurs. The reader learns about the time machine and the rules of time travel alongside Eckels. The audience even feels a bit sorry for him when it's clear that he is super scared. He knows that he has gotten himself into a situation that he is under prepared for. Chances are most readers can empathize with that feeling.
The antagonist is a bit harder. I've always thought that Eckels makes a great antagonist, too. His attitude, right from the start, is flippant and cavalier. It's clear that he is not taking Travis's warnings seriously enough.
"So they're dead," said Eckels. "So what?"
I also view him as the antagonist, because it's his fearful freak out that put everybody else in danger. He loses his head so completely that he leaves the floating path of time traveling awesomeness and steps on a butterfly. He's the reason that all of the present is completely different when everybody returns. He's the guy that ruined the present/future.
If you are not allowed to list Eckels as both, list time as the antagonist. That's simple enough to defend. Any change done in the past by time traveling humans is severely punished. That sounds like something a bad guy antagonist would do -- punish the heroes.