Quote 1
(Polyphemos, in Odysseus’ tale:) ‘“Hear me, Poseidon who circle the earth, dark-haired. If truly I am your son, and you acknowledge yourself as my father, grant that Odysseus, sacker of cities, son of Laertes, who makes his home in Ithaka, may never reach that home; but if it is decided that he shall see his own people, and come home to his strong-founded house and to his own country, let him come late, in bad case, with the loss of all his companions, in someone else’s ship, and find troubles in his household.” ‘So he spoke in prayer, and the dark-haired god heard him.’ (9.528-536)
Wounded Polyphemos invokes his father Poseidon as well as Fate to his aid in cursing Odysseus. This is excellent evidence that notions of fate and free will are not mutually exclusive. Odysseus chooses to blind the Cyclops and to reveal his name, therefore it is his fate to suffer at sea. His pride, not his destiny, determines the following course of events.
Quote 2
(Polyphemos, in Odysseus' tale:) '"Stranger, you are a simple fool, or come from far off, when you tell me to avoid the wrath of the gods or fear them. The Cyclopes do not concern themselves over Zeus of the aegis, nor any of the rest of the blessed gods, since we are far better than they […]."' (9.273-287)
Not all divinities live on Mount Olympus. You have to be careful in The Odyssey, because there's always that chance that you're inadvertently ticking off some immortal with powerful connections—like a close family tie to the god of the sea.
Quote 3
(Polyphemos, in Odysseus' tale:) '"Hear me, Poseidon, who circle the earth, dark-haired. If truly I am your son, and you acknowledge yourself as my father, grant that Odysseus, sacker of cities, son of Laertes, who makes his home in Ithaka, may never reach that home; but if it is decided that he shall see his own people, and come home to his strong-founded house and to his own country, let him come late, in bad case, with the loss of all his companions, in someone else's ship, and find troubles in his household." 'So he spoke in prayer, and the dark-haired god heard him.' (9.528-536)
Polyphemos wants revenge. But is it justice? Zeus lets it happen—for a while, at least—so we're inclined to think that maybe it is. The question is whether it's Odysseus' punishment for blinding the guy, or for being dumb enough to reveal his name.
Quote 4
(Polyphemos, in Odysseus’s tale:) ‘“Stranger, you are a simple fool, or come from far off, when you tell me to avoid the wrath of the gods or fear them. The Cyclopes do not concern themselves over Zeus of the aegis, nor any of the rest of the blessed gods, since we are far better than they […].”’ (9.273-287)
The punishment that Polyphemos ultimately suffers is justified by his refusal here to play by the rules. On the other hand, you could argue if Polyphemos and his people have chosen to live outside of Zeus’s rules, why should they be forced to comply with them? This would be like traveling to another country and chastising them for not celebrating the Fourth of July. Again, the counter-argument would be that Zeus, as the King of the Gods, rules everything and everyone without question. What do you think?
Quote 5
(Polyphemos, in Odysseus’s tale:) ‘“Give me still more, frely, and tell me your name straightway now, so I can give you a guest present to make you happy.”’ (9.355-356)
The Cyclops shows false hospitality towards Odysseus, promising him a lovely gift if he will tell him his name. Readers know that Polyphemos is untrustworthy and suspect a trick.
Quote 6
(Polyphemos, in Odysseus' tale:) '"But tell me, so I may know: where did you put your well-made ship when you came? Nearby or far off?" 'So he spoke, trying me out, but I knew too much and was not deceived, but answered him in turn, and my words were crafty: "Poseidon, Shaker of the Earth, has shattered my vessel. He drove it against the rocks on the outer coast of your country, cracked on a cliff, it is gone, the wind on the sea took it […]." (9.279-285)
Polyphemos is trying to trick Odysseus, but the man of lies is one (or two, or three) steps ahead of him. You can't play a player, especially when that player is world-renowned for his game.