In The Odyssey, what are some examples that prove that Odysseus is arrogant? I already have the part of when Odysseus yells his name to the Cyclops.

One could
reasonably argue that Odysseus shows arrogance in wanting to hear the song of the Sirens, those
strange creatures who lure sailors to their deaths against the rocks of their island. The
Sirens' song is renowned for its extraordinary beauty, which is why so many sailors cannot
resist its beguiling charm. Odysseus doesn't want his men to suffer a similar fate, which is why
he insists that they plug up their ears with beeswax when they sail past the Sirens'
island.

As for Odysseus, and this is where his arrogance comes into the
picture, he won't block out the Sirens' song; he's going to listen to it. He wants to be able to
say that he's heard their song and yet lived to tell the tale. So he orders his men to strap him
to the mast as the Sirens do their thing. No matter how much Odysseus begs his men to set him
free as he undergoes the exquisite torture of listening to the song that ravishes his ears with
its heavenly beauty, they must ignore him.

Odysseus didn't really need to
listen to the Sirens' song. As with the case of insulting the Cyclops Polyphemus and revealing
his name, he was overcome with pride, the kind of pride that only a great warrior-king can
display.