It is worth noting that, even within his adventure with Polyphemus, Odysseus shows his arrogance in more ways than one. Note that it was Odysseus who was insistent on staying in the cave in the first place, intent on receiving a gift from his would-be host, even as his followers...
It is worth noting that, even within his adventure with Polyphemus, Odysseus shows his arrogance in more ways than one. Note that it was Odysseus who was insistent on staying in the cave in the first place, intent on receiving a gift from his would-be host, even as his followers wanted to flee back to the ship. That insistence would see them captured and trapped in the cave by the cyclops to be devoured.
However, Odysseus's arrogance can be seen throughout his various adventures. Another key example can be found in his adventure with the Sirens and his insistence on listening to their song. In addition, there is his initial instinct to attempt to fight off Scylla, even going so far as to interrupt Circe with the words:
But tell the truth now, goddess," I protested.
"Deadly Charybdis—can't I possibly cut and run from her
And still fight Scylla off when Scylla strikes my men?"
First of all, when reading these interactions, you should keep in mind the very real difference in status between Circe and Odysseus, given that Circe is a minor goddess. With that in mind, interrupting her in this fashion, as she is advising him on his his homeward journey, even implying dishonesty on her part, shows an element of recklessness by Odysseus. Circe responds to his challenge by chiding his stubbornness and insistence on fighting:
"So stubborn!" the lovely goddess countered.
"Hell-bent yet again on battle and feats of arms?
Can't you bow to the deathless gods themselves?
Scylla's no mortal, she's an immortal devastation,
Terrible, savage, wild, no fighting her, no defense—
Just flee the creature, that's the only way."
Odysseus does end up heeding Circe's words, but his initial intransigence and gainsaying of a goddess can be interpreted as a dangerous display of hubris on his part.
Finally, you should take into account his overall attitude regarding both his companions and himself. For example, regarding the sacking of Ismarus, Odysseus says the following:
Then I urged them to cut and run, set sail,
but would they listen? Not those mutinous fools;
there was too much wine to swill, too many sheep to slaughter
down along the beach, and shambling longhorn cattle.
Later, when Odysseus returns to the island of Aeolus, he exclaims: "A mutinous crew undid me—that and a cruel sleep." Here, to be fair to Odysseus, it should be noted that his crew often is disloyal and mutinous, but even so, this disloyalty has to (on some level) be regarded as a failure of Odysseus's own capabilities as a leader. Regardless, in his underlying attitude, and the way he frames this narrative for his Phaeacian audience, we observe a mindset by which Odysseus is quick to spread blame onto others, refusing to hold himself accountable as their leader.