In "The Most Dangerous Game," what does it mean when Rainsford thinks "I have played the fox; now I must play the cat of the fable?"

The fox is the animal being chased.  Rainsford has been chased all across the island.  He is tired of being the "fox."  He is tired of being hunted. He says he must now become the cat in the fable.  The cat is the hunter and Rainsford deciders to begin to think as a hunter instead of being hunted.  His role is reversed.