Why is odysseus a hero?
In Greek culture, it didn’t matter so much what you did, so long as you were the best at it. The measure of a hero is that he is better than his rivals. Odysseus is the king of liars and schemers, and that’s where he derives his heroism, so episodes which seem to us the opposite of heroism (for example pretending to be insane to avoid having to initially go to fight in Troy) are actually examples of his heroic nature, and demonstrations of why he was so important to the Greeks. The primary example of this is the horse itself. Odysseus’ idea won the war through guile and deception where the more conventional heroic tactics had led to a 10 year stalemate. There’s no sense in Homer that Odysseus’ lying, scheming, conniving ways were in any way regarded as undesirable characteristics – the point is always how good Odysseus is at it.