What are Odysseus' strengths and weaknesses and how do they show on Helios' Island?
The events on Helios Island take place in Book 12 of the Oddyesy.
Circe tells Odysseus that no one has heard to the 'song of the sirens' and lived. He uses guile, bravery and inventiveness, to pass through.
Circe also gives him instructions on how to return home. His ship must pass a monster, immovable rocks, or whirlpool. While Circe suggests sacrificing a small number of men, in order to pass the monster. Odysseus remains loyal to his crew, remaining indecisive as to the 'best' strategy.
Upon approaching the monster, Odysseus arms his men, preparing for a fight. This shows a brashness and reactive nature - remember he has been warned to pass quickly (leaving the sacrifices).
Circe's last warning was to avoid taking the cattle of Helios. In fact, he's been warned to stay away all together (several times). Despite this, and his crew wanting to mourn lost crew-mates, his curiosity, or sense of immortality, take him to the island.
Overall Odysseus comes across as a brave, risk taking, explorer. His crew are loyal, and together they have fought great foes. However, Odysseus seems to enjoy flirting with danger - routinely dismissing good advice, in order to test himself.
One can argue that the episode on Helio's (Apollo's) island illustrates on of Odysseus' important strengths that, ironically, is also a weakness.
When Odysseus and his crew approach the island of Helios, even though Odysseus has been told to avoid the island, Odysseus gives in to the pleading of his men to land in order to seek food and water. On the surface, Odysseus' decision to go ashore seems to be a seriously bad leadership decision, but we need to keep in mind that Odysseus and his crew have been together for over twenty years--through the Trojan War and tremendous struggles to get back to Ithaca. His crew are not just subordinates, but companions, and several have been his close advisers all his life. His decision to go ashore on Helios is based on compassion and, more important, trust that his men will follow his instructions.
Odysseus' compassion--and trust in his men--are strengths as long as his men follow his instructions. These same traits, however, become weaknesses only in hindsight--when his men betray his trust--and the Helios island episode becomes an example of a strength that evolve into weakness. A hallmark of Odysseus' leadership in both the Iliad and the Odyssey is his flexibility in thought and deed. This flexible leadership style, however, is dependent upon everyone doing his duty and, on the island of Helios, this particular strength is also a weakness.
Odysseus is a very curious, strong, resourceful, smart, and determined man. That said, he is also stubborn, defiant, proud, and full of hubris, all traits which often get him in trouble.
Odysseus was warned by Circe to stay away from Helios' island. However, his men's complaints and his curiosity and defiance got the better of him, and he allowed his men to land the ship there. Once on the sun god's island, Odyseus' men disobeyed him and ate the god's cattle. Zeus then hurled a thunderbolt at their ship and it is only through Odysseus determination and strength that he survived.