In The Odyssey, why does Odysseus offer the Cyclops the liquor he brought from the ship?
When the Cyclops returns to his cave, he closes the cave with a huge boulder. As a result, Odysseus and his men are trapped inside, and to their horror, the Cyclops turns out to be less than inhospitable. The Greeks expected guests to be treated kindly, to be offered food, drinks, and gifts, but the Cyclops disdains the customs and even declares he has no fear of the gods. He snatches up a pair of Odysseus' men and eats them! After another day, he has eaten four more men.
Realizing they are all likely to die, Odysseus puts his wily mind to use. He offers the Cyclops the potent wine so that he can make Polyphemus drunk, so drunk he will fall asleep. The wine is delicious and the Cyclops asks for more, drinking so much he does pass out. When he is soundly asleep, Odysseus and his men blind the Cyclops by stabbing him in his eye with a sharpened, heated olive pole. Although the Cyclops screams for help, because Odysseus has told him his name is "Nobody," when the other Cyclopses ask who is hurting Polyphemus, he answers, "Nobody." So they figure nothing is wrong.
Once the Cyclops is blinded, the men stand a better chance of escape. The next day when the Cyclops opens the cave to release his sheep, the men hide under the wooly sheep and leave safely.
To add a bit more to Cybil's post. The liquor is very good, so the Cyclops will want more of it. Since Odysseus and his men are trapped inside the cave, they cannot kill the Cyclops, so they decide to blind him instead.
Odysseus gives the Cyclops a false name while the Cyclops is drunk. So, after he is subdued and they stab his eye, the only name he can remember is "Noh,bhdy" or Nobody.
It is very clever of Odysseus to offer the drink to the Cyclops because it enabled his men and himself to gain an advantage over the larger and more powerful enemy.