Odysseus, the hero from Homer’s epic poem The Odyssey, does not kill the brutish cyclops, Polyphemus, because Odysseus and his men would be trapped in the cave.
“Then he rolled a huge stone to the mouth of the cave—so huge that two and twenty strong four-wheeled wagons would not be enough to draw it from its place against the doorway.”
Odysseus and his men, though strong, would not be able to move the stone that closes off the cave. Only Polyphemus would be able to move the rock. This is a moment in the text that reveals Odysseus as not just brave but wise. Even full of rage after the killing and eating of his crewmen Odysseus keeps his rational mind as noted in the following quote.
“…he stretched himself full length upon the ground among his sheep, and went to sleep. I was at first inclined to seize my sword, draw it, and drive it into his vitals, but I reflected that if I did we should all certainly be lost, for we should never be able to shift the stone which the monster had put in front of the door.”
Provided with the opportunity and means of killing off the beast, Odysseus knows better and has to come up with a better means of escape. Here Homer provides the perfect opportunity for the hero Odysseus to show his true wisdom.
Although Odysseus is sure he can kill the Cyclops, there is one major problem: the rock used as a door to the Cyclops's cave is so heavy that it can only be moved by someone as large and strong as the Cyclops himself. If Odysseus kills the Cyclops before he has moved the rock then Odysseus and his men will still most definitely die in the cave. To get around this issue, Odysseus comes up with his infamous plan of getting the Cyclops drunk, spearing out the Cyclops's eye, and tying his fellow shipmates to the bellies of the Cyclops's sheep. Eventually the Cyclops lets the sheep out to graze and the men are able to escape.