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Polyphemus hates nobody more than he hates Odysseus. Odysseus blinded Polyphemus, so the Cyclops holds a deep grudge against him.
Blinding Polyphemus allows Odysseus and his men to escape from the cave without being detected by Polyphemus. Killing him would have likely alerted the other Cyclopes and made their escape more difficult. Additionally, blinding him adds an extra layer of humiliation and revenge for the harm Polyphemus inflicted on Odysseus and his crew.
Odysseus doesn't kill Polyphemus immediately because he needs him to move the giant's boulder from the entrance of his cave. Additionally, Odysseus hopes to escape being eaten by the cyclops and believes he has a better chance of surviving if he outwits Polyphemus rather than confronting him directly.
Polyphemus is easily outwitted by Odysseus when the latter tricks him by giving a false name ("Nobody"). Additionally, Polyphemus falls for Odysseus' plan by believing that the sheep in his flock are actually his men escaping. Lastly, his boastfulness and lack of insight make him vulnerable to Odysseus' cunning tactics.
One example is when Odysseus outsmarted Polyphemus by devising a plan to escape from his cave by blinding him and then hiding under the sheep to leave undetected. Another example is when Odysseus tricked Polyphemus by giving him a false name, leading the Cyclops to underestimate him and not see through his deception.
Odysseus does not leave the cave of Polyphemus when his men ask because he wants to see if the cyclops will offer them hospitality, as is the custom in Greek culture. He also wants to test the strength of the cyclops, believing that only he has the power to move the boulder blocking the entrance. Additionally, Odysseus hopes to outwit and defeat Polyphemus rather than flee.