Why does Odysseus refuse to take the food and animals from Cyclops, in Book IX of The Odyssey?
The answer to this question reveals some of the social customs of the heroic age of Ancient Greek poetry. It was a mark of high social status to receive gifts from a mighty host, and preferable to stealing. A man receiving a gift from a host of high status and power gains not only the gift, but increased status as well. Odysseus keeps this in mind as he enters the Cyclop's cave and sees all his cheese and livestock. Odysseus said of the Cyclops "I wanted to see himself and claim the stranger's gift" (Rouse 98). It was customary, upon receiving strangers in one's home, to give them gifts; and Odysseus wanted to invoke this privilege from the towering Cyclops.
Odysseus is displaying a bit of bravura in front of his men, too. They suggest stealing some of the sheep and goats and cheeses, but Odysseus, their leader, does not allow them. Odysseus wants to prove that he is brave enough to face the huge, lawless Cyclops, and claim a customary guest-gift. He regrets this decision later, however, as the Cyclops devours four of his men and calls down the curse of Poseidon on him.
Source: Homer, The Odyssey. W. H. D. Rouse, trans. New York: Mentor, 1950.