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.