he Odyssey, does not kill the brutish cyclops, Polyphemus, because Odysseus and his men would be trapped in 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.
Odysseus and his men were trapped in a cave by Polyphemus, the cyclops. Polyphemus has a physical strength that even the combined strength of Odysseus and all his men could not match. Using that strength, Polyphemus closed the Cave with a gigantic rock. In order to escape, they need Polyphemus to open a passage first. If killed, Odysseus and his men wouldn't be able to move the rock. They'd eventually die inside the cave.
