Sometimes, Odysseus really acts like a hero, but sometimes not. In the Trojan War, he was very strong and brave, and he protected his men, but in book 9-12, he doesn’t seem to be the leader of his crew because they decide against his warning more than once. In book 11, he gets scared of the spirits of the dead and runs away.
Furthermore, in my opinion it is never right to kill people, not even in a war. So, though it was to save his crew, it is not honorable to kill people.
In book 9, several men were devoured by the Cyclops in front of his eyes simply because of Odysseus’ pride.
He is not a good role model because he is not faithful to his wife. In book 10, he cheated on her with Circe to make her release his men. He also cheated on her with Calypso.
He seems to be selfish, for example in book 12, when he tells his crew about what Circe told him about the sirens. He tells them: “I alone was to hear their voices, so she said, but you must bind me with tight chafing ropes so I cannot move a muscle, bound to spot…”(276 Homer), but she actually told him: “Soften some beeswax and stop your shipmates’ ears so none can hear, none of the crew, but if you are bent on hearing, have them ties you hand and foot in the swift ship, erect at the mast block, lashed by ropes to the mast so you can hear the Siren’s song to your heart’s content” (273 Homer).
On the other hand, he is clever, and he is helped by the gods. That makes him different from normal people. Athena really likes him and is his mentor. She is convinced that he is a hero. Also, the author, Homer, who is a god, too, seems to think of Odysseus as a hero.
He also seems to be kind of famous because many