Odysseus ignores his men’s pleas to return to the ship. As a result, they face terrible consequences. How does Odysseus’s decision defy ancient Greek attitudes and values?
Odysseus's choice to not only remain on the Cyclops island but also to angrily proclaim his identity to the Cyclops is an example of hubris or pride. Despite the entreaties of his shipmates to quickly depart from the island and not engage with Polyphemus, Odysseus is proud enough to assume that he is control of his interaction with the giant; in the end, he gets played and his men suffer from his arrogance. Then, angry that he was tricked and his men have suffered, he unnecessarily yells his name back to Polyphemus, with the epithets that he is a "raider of cities" and that he is from Ithaca are meant to further glorify himself, but it is pride and it will backfire on him eventually.
This pride, or hubris, goes directly against Greek values. The Greek believed that hubris was a sin; humans were below gods in the hierarchy of power and to show hubris was to equate oneself with a god. Therefore it was sacrilegious. In Greek tragedy, the protagonist or tragic hero was brought down by his own hubris. For example, Oedipus is so proud he decides to go against prophecies, believing he is more powerful and knowledgable than the prophets. As a result, he falls victim to the prophet and experiences his downfall. The fate of Odysseus's men is the downfall of his own pride.
On the Cyclops' island, Odysseus sees that the owner of this particular cave has a large flock of sheep, crates loaded with cheeses, pens full of goats, and vessels overflowing with milk and whey. His men "pressed [him] strongly to take some cheeses and go back [...] But [he] refused [...]," hoping that he might meet the owner of all these goods and that "he might offer gifts." Odysseus is hopeful that his host will offer him a gift because of the Greek value of a reciprocal host-guest relationship. They believe in the importance of hospitality, and they also believe that Zeus protects travelers; therefore, it was thought to be a religious imperative to offer hospitality. To care for a traveler was to appease and please the most powerful of the gods. However, the traveler is also supposed to be grateful and gracious (and not take advantage of his host), and Odysseus seems to expect a gift from his host in addition to eating his and his crew's fill of their host's food. His insistence that the crew wait around, helping themselves, to see if the cave's owner would give him something more breaks with the spirit of the host-guest relationship and thus defies the Greek value of hospitality.