How we cite our quotes: (Chapter.Paragraph)
Quote #1
Piper's snowboarding jacket was flapping wildly, her dark hair all in her face. Jason thought she must've been freezing, but she looked calm and confident—telling the others it would be okay, encouraging them to keep moving. (2.6)
This is very early in the book—Piper doesn't know she's a demigod, and doesn't know she can persuade people, but she's still trying to take care of everyone. Also note that Piper almost certainly wouldn't see herself as calm and confident. Jason sees her courage more clearly than she would.
Quote #2
"Spirits, fear me!" Hedge bellowed, flexing his short arms. Then he looked around and realized there was only Dylan.
"Curse it, boy!" he snapped at Jason. "Didn't you leave some for me? I like a challenge!"
Leo got to his feet, breathing hard. […] "Yo, Coach Supergoat, whatever you call yourself—I just fell down the Grand Canyon! Stop asking for challenges!" (2.55-57)
Leo could be talking to the author here. The book is just one long series of challenges, after all, and while it makes for an entertaining read it's pretty rough on the characters. You can see where even a brave guy like Leo might find it a little tiresome over the course of five hundred pages.
Quote #3
He could turn around now and tell everyone he'd been joking. Psych! Nyssa could go on the quest instead. He could stay at camp and learn to be part of the Hephaestus cabin, but he wondered how long it would be before he looked like his bunkmates—sad, dejected, convinced of his own bad luck. (11.65)
The alternative to courage and standing up for your friends here seems to be bad luck and dejection. Courage is its own reward in part—which perhaps unintentionally undermines courage. After all, if you're better off being courageous, is it really courage? Wouldn't Leo seem more courageous in going if staying behind would be a cheerful prospect rather than a gloomy one?