How does Odysseus's arrogance help him throughout the Odyssey?

Let's make one thing clear: Odysseus's arrogance is one of his least admirable traits—but it is part of what makes him heroic. For starters, it imbues him with great confidence. Being confident is a hallmark of heroes. Think about it: You never see Wonder Woman doubt whether or not she can land her invisible jet. We're pretty sure LeBron James never said, "No, Coach. Why don't we let Mo Williams take the last shot?"
Like the mightiest MCs, Odysseus possesses an arrogance that also makes him a skilled self-promoter, which only further boosts his reputation as a hero. When he takes all the credit for himself and his men escaping from the Cyclops, or when he claims that he's the greatest archer since the invention of the bow and arrow, he's serving as his own hype man. If Odysseus doesn't try to spread the word about his towering greatness, how else will his story get out there? It's not like he can post photos of himself and his men raiding Ismaros on Instagram. If Odysseus wants to become a legend, he needs to takes risks and, when they pay off, tell everybody to remember his name—even if it does mean being cursed by Poseidon.