Odysseus has one choice to make, either go through a path of rocks, or go through the land of the Scylla and Charybdis. All the men are scared but they believe in Odysseus to make the right call. Odysseus told his men that he can get them through this like he did in the cave with the cyclops.
Odysseus knew that the rocks would destroy the ship and everyone on it, but he realized that if he went towards the Scylla and Charybdis there is still a possibility of them surviving. So he went towards the monsters, very carefully, and cautious. He knew that he had to avoid Charybdis with all his power.
Odysseus was drifting towards Charybdis so he and the crew started steering away and, actually got away, until Scylla popped up. Scylla snatched up 6 of his men, then to do same thing again a couple seconds later.
He shows curiosity by wanting to know what these monsters really are, and as well as leadership to risk loosing some of his crews lives and a possibility of his own.
Odysseus chose the correct path. Because he chose to go through the monsters, a lot of his men still survived, and were able to go a little further.
Odysseus gets all of his men on rows and paddle away from all danger, and they were free at last, for now...