George Milton fears that his long-time friend and travelling companion, Lennie Small, will one day get them both into deep trouble. In fact this has already happened on previous occasions prior to the start of the novel, but the worst incident occurs near the end of the story, when Lennie ends up killing Curley's wife purely by accident.
The trouble is that Lennie is both mentally backward and physically very strong. He is not aware of his own great strength; he cannot control it. He kills Curley's wife most inadvertently by snapping her neck after she invited him to stroke her hair, to feel its softness. He just likes to pet soft things, by his own admission, but he ends up petting too hard. Earlier in the story he accidentally kills his pet puppy in the same way. George also remembers how they were recently chased out of town after Lennie tried to pet a girl's dress; she thought he was trying to rape her. In the incident with Curley's wife, he gets confused when she tells him that he's messing her hair up; instead of letting go, he just hangs on and ends up shaking her to death. But the story makes quite clear that he never meant to hurt her at all.
George is always worried about the prospect of Lennie getting into trouble, but he never leaves him. On the contrary, he is the more resolved to protect him, because, as he says to him: 'Somebody'd shoot you for a coyote if you was by yourself.' Lennie simply wouldn't be able to survive on his own; he needs George. But George needs him too; he is a good-hearted, affectionate friend. Their friendship is something of a wonder to the other itinerant ranch workers who generally travel alone. But Lennie and George are the exception, and because they have each other, they do not suffer from the same degree of loneliness that other migratory workers do.
In spite of everything, then, George sticks by Lennie. When finally Lennie is being hunted down for the murder of Curley's wife, George shoots him in an act of compassion, to prevent him being lynched or incarcerated.