Why did George feel he needed to kill Lennie?
George and Lennie have a long-standing bond, George acting as Lennie's guardian. Referred to throughout the book as a child or an animal ("(Lennie) walked heavily, dragging his feet a bit, the way a bear drags his paws"), Lennie possesses the mental ability of a child, yet is described as having the strength of a "bull". When George discovers that Lennie has killed Curley's wife accidentally while attempting to just stroke her hair, it is apparent that Curley and the other hands from the ranch will lynch Lennie, and he will be beaten brutally and killed.
The scene in Chapter Three displaying the men trying to convince Candy to shoot his dog, is significant in foreshadowing the final climax. It ends with Candy lamenting not making the difficult decision to take full responsibility for this life:
"I ought to of shot that dog myself, George. I shouldn't ought to of let no stranger shoot my dog." (Chapter 3, Page 61)
George tackles a dilemma, and acting in love, makes the decision to end Lennie's life in order to save him from a violent, lonely death. The two have always been together and Lennie's life ends with his friend George there, still ultimately bonded in the relation of their shared dream of "livin off the fatta the lan". And thus, George is aware that they can run no further and the American dream dies as the friendship has to at that moment.
George wants to save him, and the only way to save him is to to kill him. George, unlike Lennie, knows the type of people that live their life. He knows the fate of Lennie because he has seen it mirrored in Candy's dog.
George doesn't want to have the same regret...he wants to do it himself so it can be done kindly.
George and Lennie's relationship is one of complexity and although many readers cinsider this as 'friendship' - this is too simplistic an assumption. George has the position of being a 'foster' carer to an adult child. The shooting of Candy's dog was a bitter blow for the character to swallow - yet Steinbeck places the emphasis on his remark "I should a shot him" - thus when Lennie can no longer be kept out of the grasp of society and its laws George steps up to the mantle to do the one thing he can. Remove Lennie from harm. He had very little choice - and as the title suggests 'many a slip between cup and lip'.