Why does Eckels want to go back in time in "A Sound of Thunder?"

In Ray Bradbury’s short story “A Sound of Thunder,” Eckels wants to go back in time to hunt dinosaurs because he is what is commonly called a “trophy hunter.” Trophy hunters are those who crave the opportunity to hunt and kill rare or endangered species or animals the accessibility of which exist outside the realm of the norm, as when Americans or others travel to Africa or Asia for the purpose of killing animals foreign to the United States. For such individuals, the opportunity to hunt a long-extinct species, such as dinosaurs, especially dinosaurs known to have been particularly ferocious, would be too hard to resist. Such is the case with Eckels.
In Bradbury’s story, Eckels arrives at the corporate office of the company that has developed a time machine and that uses it to offer expensive hunting excursions to the distant past. Such excursions involve considerable risk, from accidental death or from being consumed by one’s prey or, most dramatically, from altering the course of history. Eckels has been passionate about the outcome of a major election, the result of which went his way. As he is contemplating the risks of the hunt and the catastrophe that would have materialized had the opposing candidate won, Eckels is assured by an employee of the company that all he has to focus on at the moment is his hunt, not the risks associated with the hunt or any hypotheticals emanating from the recent election. Evidence of Eckels’ motivation is present in the following exchange between him and the employee:

“. . . Keith’s President now. All you got to worry about is—”
“Shooting my dinosaur,” Eckels finished it for him.

Eckels wants to kill a dinosaur solely for the experience of hunting such rare and dangerous prey.

Eckels wants to be able to shoot and kill a dinosaur: something he could hardly do without traveling back in time. He has made arrangements with the business called Time Safari, Inc.., and is paying $10,000 for the experience. The year is 2055. This is Eckels’ first foray into time travel. It’s unclear whether or not he has hunted animals before. But obviously the chance to see and kill a Tyrannosaurus rex has grabbed his interest. As soon as he enters the Time Safari office, however, his nerves are already starting to get the better of him. Once the time machine takes the hunting group back to the prehistoric age and landscape, his apprehension quickly grows to terror. Killing a dinosaur isn’t quite as easy or as fulfilling as he expected.