Why does Odysseus want to stay in Polyphemus's cave even though his men press him to leave?
Even though his men want him to take some food and leave as soon as possible, Odysseus wants to stay in Polyphemus's cave because he hopes "[he] might see [the cave's owner] and [this owner] might offer [Odysseus] gifts." Odysseus might expect such gifts from an obviously wealthy host because of the ancient Greek ideas concerning hospitality. Greeks believed Zeus protected travelers and that a host had a religious obligation to offer hospitality to any traveler; this hospitality would often include the presentation of a guest-gift, if such a gift were financially viable for the host. Odysseus isn't just randomly expecting presents; rather, he's expecting (perhaps a tad arrogantly) that he will be offered gifts as an extension of this hospitality. The guest, however, also had an obligation not to take advantage of a host's hospitality, and so we might read Odysseus's expectation as a bit presumptuous.