In Homer’s epic poem “The Odyssey,” Odysseus and his men become trapped in the cave of the Cyclops Polyphemus. The Cyclops traps them in the cave by rolling a large boulder across the entrance, which only he could move.
While the Cyclops was out tending to his flock, Odysseus devised a plan to blind him using a wooden stake that they had sharpened and heated in the fire. When the Cyclops returned and was blinded, Odysseus and his men hid themselves under the bellies of the Cyclops’ sheep, which he let out of the cave the next morning. This allowed them to escape the cave without the Cyclops knowing.

However, to answer the original question, Odysseus did not kill the Cyclops because he knew that the boulder blocking the cave entrance was too large for them to move. Killing the Cyclops would not have solved their problem of being trapped in the cave, and it would have likely led to them being killed by the Cyclops’ fellow giants.
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