Symbolism, Imagery, Allegory
Noah's dad is a manly man—the kind of dad who makes "every other kid on the beach with their flimsy fathers out of their minds with jealousy." (3.135) Um, we're not jealous, but thanks.
Noah, on the other hand, has always been skinny and timid and totally uninterested in athletics. When he was a kid his dad tried to make him learn how to swim by throwing him into the ocean—and Noah sank right to the bottom. No wonder he's in danger of drowning all the time.
"The first Broken Umbrella Talk happened that night," Noah recalls. "You need to be brave even when you're afraid, that's what it means to be a man." (3.146) Yawn.
Noah's dad couldn't conceive of his son as still an awesome dude, but different (at least then). Instead, he saw him as deficient. Nonfunctioning. Useless. "Act tough and you are tough, as Dad has said and said and said—like I'm some kind of broken umbrella." (1.7) The umbrella, of course, is a symbol for masculinity, and in the eyes of his father, Noah's isn't working right.
It's a sad image, right? What's more of a bummer and a disappointment than a busted umbrella when it's raining outside?
Apart from thinly veiled homophobia, of course. Duh.