How do books 6–8 of the Odyssey show Odysseus as a leader?

In books 6–8 of the Odyssey, Odysseus is the honored guest of the Phaeacians. During this part of the poem, Odysseus doesn't get to do much that's especially heroic. It's only later on, in books 9–12, when Odysseus tells his awestruck hosts about his epic wanderings, that his leadership skills are revealed in all their majestic glory.
Before then, however, Odysseus does at least show that he's no ordinary mortal. The Phaeacians are renowned for their athletic skills, and an impudent young man by the name of Broadsea openly mocks Odysseus and challenges him to a display of athletic prowess.
Now at this point, Odysseus could simply make some kind of excuse and back down. After all, he hasn't yet revealed his identity and wants to keep it a secret for as long as possible. He knows that if he participates in the athletics contests, then he'll wipe the floor with the competition, potentially exposing himself as the hero that he is.
But Odysseus just wouldn't be Odysseus if he didn't grab an opportunity to show what he's capable of. There's no way in a million years he would ever back down from any kind of challenge. Among other things, Odysseus is a leader, and leaders lead by example. So in response to the impudent young man's foolish challenge, he picks up a discus and throws it farther away into the distance than anyone else could possibly manage.