After George expresses the built-up anger and frustration he feels because of being tied to a man who causes him so much trouble, Lennie offers to go away and live by himself.
"If you don't want me, you only jus' got to say so, and I'll go off in those hills right there--right up in those hills and live by myself. An' I won't get no mice stole from me."
George's response is:
"I want you to stay with me, Lennie. Jesus Christ, somebody'd shoot you for a coyote if you was by yourself. No, you stay with me. Your Aunt Clara wouldn't like you running off by yourself, even if she is dead."
George realizes that Lennie is incapable of looking after himself. He would starve to death if he tried living alone in a cave. Besides, George still feels obligated by the promise he made to Aunt Clara to look after Lennie. But this disagreement between the two men is an early sign of a change in their relationship. George is beginning to feel that it is too much for him, in these hard times, to have to look after somebody besides himself. It is hard enough for George to find a job for himself without having to find two jobs. We see in the next chapter the trouble George has with the boss at the ranch. The boss becomes suspicious because George does all the talking. They are in danger of losing the jobs they thought they had already been given in San Francisco at the employment agency. And George is worried about Lennie's behavior. That incident with the girl in Weed may have been the worst trouble Lennie has ever caused for both of them. They could easily have gotten killed.
For his part, Lennie is beginning to feel rebellious. When George tries to take his dead mouse away, Lennie puts up a strong resistance. He is beginning to realize that he has a will of his own and can say "No!" He has a child's mind, but he seems to be becoming a slightly older child, perhaps like an adolescent who wants more independence. He resents having to do everything George tells him to do, just like many adolescents who rebel against their parents.
This scene by the river foreshadows future trouble. George can't be watching Lennie all the time, and Lennie inevitably gets into trouble. He is especially dangerous because he doesn't know his own strength. It would seem that the partnership between these two men is bound to break up. It happens when Lennie kills Curley's wife in the barn. But something else would have happened sooner or later.