Based on Odysseus's criticism of the Cyclops, what kind of society do you think the Greeks valued?
The Greeks very much valued hospitality. In fact, it was somewhat of a religious imperative because Zeus was the god of travelers, and they believed that he offered protection to those who were far from home. Thus, if you were kind and hospitable to any strangers who came to your home looking for shelter, food, and the like, you were actually paying homage to the most powerful of the gods. This religious imperative was called xenia, and it entailed a reciprocal relationship between guest and host. The host should offer what he could to any guest, and the guest should never take advantage of the host's generosity and should try to offer something in return if he were able.
Because of this tradition, Odysseus and his men expect that whoever lives in the cave they find will automatically share his food and supplies. Odysseus brings a skin of wine as a gift for whoever this person is as well. When the cyclops, Polyphemus, returns to his home and finds the men eating and drinking, he says that he doesn't fear Zeus at all nor have any reverence for Zeus's traditions. He then proceeds to eat two of Odysseus's men (and he eats a total of four more before the men eventually escape).
Odysseus's criticism of the cyclops for his violent response to what the Greeks' view as a reasonable expectation shows just how prevalent this concept of xenia was. It shows us that the Greeks valued hospitality and reciprocity in a world that, if inhospitable to travelers, would very seriously limit all possibility of travel. Those communities or characters in this poem who do not offer hospitality are all monstrous, and Polyphemus is no exception.
In comparing and contrasting Odysseus with the cyclops Polyphemus, it becomes rather apparent that the Greeks valued intelligence over brute strength. Despite his gigantic stature, Polyphemus was defeated by Odysseus simply because Odysseus was smarter. Had it not been for Odysseus' arrogance in revealing to Polyphemus that it was he, Odysseus, who had blinded him, Polyphemus would have never known whom to blame. One could also look at the race of the Cyclopes as a whole as a condemnation of a life lived without law, order, or civilization. The Greek audience of Homer's tale would have certainly been appalled at the inhospitable and barbaric creatures who enjoyed only the most basic and carnal of human pleasures: food, drink, and violence.