Why does Eckels want to travel back in time?

Eckels wants to travel back in time to hunt and kill a dinosaur.  
Eckels is paying ten thousand dollars to be a part of a safari group going back in time.  The company that does this is Time Safari, Inc., and the expedition is being led by Mr. Travis.  
Eckels is not a character that readers are meant to like.  From the moment that we are introduced to him, it is clear that he is pompous and arrogant.  He waves around his check like it's a talisman of power and privilege.  

The muscles around  his mouth formed a smile as he put his hand slowly out upon the air, and in that hand waved a check for ten thousand dollars to the man behind the desk.

Eckels doesn't seem to realize that he will not be the only paying customer on the safari, because he uses "I" a lot instead of "we."  At one point, rules are being explained to Eckels about what he does and does not have to worry about.  He rudely interrupts the other man and says the only thing he (Eckels) has to worry about "is shooting my dinosaur."  Notice how Eckels believes that his check guarantees himself shooting rights.  
Of course as the reader comes to learn, Eckels is all talk.  Despite his brave bravado, he is the only safari member that runs in fear back to the time machine.  The T. rex is simply too scary for him.  

"Get me out of here," said Eckels. "It was never like this before. I was always sure I'd come through alive. I had good guides, good safaris, and safety. This time, I figured wrong. I've met my  match and admit it. This is too much for me to get hold of." 

He's so scared in fact, that he steps off of the path, kills a butterfly, and changes the future/present forever.