Eckels is shot by Travis because he stepped on the butterfly and changed the future.
At the beginning of the story, Eckels asks a prophetic question.
"Does this safari guarantee I come back alive?"
Of course, they tell him they can’t. He is nervous about hunting dinosaurs, but they explain the process and he goes along. He is warned not to step off the path, but he accidentally kills a butterfly. Travis is very angry.
When they return to the present, Eckles finds out that the spelling on the sign has changed and a different person has been elected president. Since this man is supposed to be a tyrant, we get the idea that Eckels has messed up the future.
Eckels moans, wanting to know if he can go back to the past and fix his mistake. Travis says nothing, but answers with his gun.
He did not move. Eyes shut, he waited, shivering. He heard Travis breathe loud in the room; he heard Travis shift his rifle, click the safety catch, and raise the weapon.
Eckels is shot more in revenge than punishment, because there is nothing that can be done. Simply by killing a butterfly, he has altered the future significantly. It is a lesson in how actions can have widespread unintended unforeseeable consequences.
The short answer to this question is: We don’t know for sure. What we do know is that a group of hunters went back to prehistoric time with the Time Safari leaders to shoot and kill a Tyrannosaurus rex that would have been downed by a falling tree anyway. They have taken every precaution to make sure that any action they take in the past will not affect the future in any way. Hunters are told to stay on the path and to not touch anything. Unfortunately, Eckels is so traumatized by the sight and sound of the huge creature that he heads back to the safety of the time machine without paying any attention to what he is doing. When the group returns to the present day, they see that both life and language have changed. It turns out that Eckels accidentally stepped on and killed a butterfly. Group leader Travis is seething with fury. We read the lines that show that Travis readies his rifle for firing. Then the story ends aptly and abruptly with “a sound of thunder.” Travis killed someone, but who? Did he kill Eckels for his mistake? Or did he kill himself, so that he wouldn’t have to answer to authorities about the grave error, and so that Eckels would have to live with the responsibility of what he’d done? Only the reader can decide.