In the short story "A Sound of Thunder," why doesn't Eckels want to kill the dinosaurs?

Eckels does not want to kill the dinosaur because it looks too big to kill.

Eckels hires Time Travel Safari, Inc. to take him into prehistoric times to kill a dinosaur.  Eckels is an experienced hunter, and he wants something more challenging.  Travis explains to him that they are not responsible for his safety, and that if he wants to back out he should.

“…We don’t want anyone going who’ll panic at the first shot....

Eckels does not want to kill the dinosaur because it looks too big to kill.

Eckels hires Time Travel Safari, Inc. to take him into prehistoric times to kill a dinosaur.  Eckels is an experienced hunter, and he wants something more challenging.  Travis explains to him that they are not responsible for his safety, and that if he wants to back out he should.

“…We don’t want anyone going who’ll panic at the first shot. Six Safari leaders were killed last year, and a dozen hunters. We’re here to give you the severest thrill a real hunter ever asked for. Traveling you back sixty million years to bag the biggest game in all of Time. ...”

Eckels is told that he has to stay on the path, and that they have a gun that will bring the dinosaur down.  The dinosaur they have selected was about to die anyway.  As long as Eckels only kills only this dinosaur, they will be fine.

When Eckels sees the dinosaur, he is shocked.  It is unlike anything he has seen before.  It is so big that he feels as if it could touch the moon.  When it comes time to kill it, he freezes.

“It can’t be killed.” Eckels pronounced this verdict quietly, as if there could be no argument. He had weighed the evidence and this was his considered opinion. The rifle in his hands seemed a cap gun. “We were fools to come. This is impossible.”

Eckels tells them to get him out of there.  When he hunted before, he was always sure he will get out alive.  Now he is terrified of the dinosaur and not sure of himself.  Lesperance tells him to hide in the time machine.  Travis and Lesperance kill the beast, and that should have been the end of it.

After Eckels is forced to remove the bullets from the dinosaur, he goes back to the time machine.  When they return to the present, everything is changed.  They realize Eckels stepped on a butterfly by accident and changed the future.