To back up #5, I think the event with Charybdis and Scylla that comes straight after the sirens definitely can be used to support the idea that Odysseus is not a hero. Note how he deliberately ignores the advice of Circe in not fighting them and tries to win even more glory and honour for himself. As a result, six men die a terrible death because of his arrogance. Not a very heroic thing to do, really.
I would take issue with his hero status because he dallies with the sirens. I personally don't like that and it always makes me dislike Odysseus, although the Sirens were alluring and supposedly no man could resist their songs. I personally don't buy that LOL.
Generally speaking, Odysseus does not demonstrate heroic qualities of manliness, wisdom, or faithfulness. Although he leaves the Trojan War with a well-deserved reputation as a fine warrior, the first time the reader sees him, he sits on the shore on Ogygia (Calypso's island), staring off at the sea and weeping because he's homesick. Heroic behavior? On a number of occasions, he loses men or loses time because he doesn't make wise choices. Greed leads to the attack on the Cicones, and he loses half of his ships. Foolish curiosity leads him to investigate the cave of the Cyclops where he loses 6 men. Failure to delegate responsibility and to tell his men what's in the bag of winds causes his ship to be blown back to Aeolia when he falls asleep because he was trying to pilot the ship alone. On the Island of the Sun-God, he tries to stay awake to prevent his men from eating the cattle so when he goes to pray, he again falls asleep, and the men cause their own doom by defying Helios' order. Finally, he is not faithful to Penelope bvecause he sleeps with every beautiful female he encounters while she waits patiently and faithfully for him on Ithaca. None of these behaviors are typical of a hero.
Just kidding guys
He is a hero in a way but I'd say that he's not a hero because of the way he acts in certain situations. Those situations, like the one with the cyclops, are inexcusable. He acted very offensivly to the cyclops, personally i would have let him eat me. The poor guys been in a cave his whole life, he's lonley and hungry. Now the cyclops has to live with no eye because Odysseus was acting in a non-heroic way.But whtev he is soooo not MY hero! He sooo totally will like NEVER be.