The first time Odysseus showed his arrogance is when he won the battle at Troy. He yells out to the gods that he doesn't need them. Also, he does not give a sacrifice to the gods for helping the Greeks win the victory. This is arrogant behavior. This is arrogant because it shows that he doesn't need the help of the gods. In return for his arrogance, the gods create a difficult journey home for Odysseus.
Also, Odysseus shows his arrogance again when he blames the situation solely on his men. He calls them mutinous fools. In book nine, on page 213, line 50, Odysseus talks of his crew cruelly:
"Then I urged them to cut and run, set sailBut would they listen? Not those mutinous fools.Too much wine to swill, too many sheep to slaughter."He blames the situation completely on his crew, taking no responsibility like a mature person, and as the crew's captain.
"Cyclopes-If any man on the face of the earth should ask youWho blinded you, shamed u so,- say OdysseusRaider of cities, HE gouged your eyes."
He yells back at the cyclops.
When he decides he can handle listening to the Sirens, but the rest of the crew need to be "protected" from it.