We could get all Freudian, but we're going to focus another way the fishing rod is symbolic: it stands for Joe's relationship with his father.
First things first. When Joe breaks the news to his dad that he wants to go fishing with Bill Harper, his dad, instead of being sore about it, offers to let them use his expensive rod. "There was nothing his father treasured more" (9.5), Joe says, so it's a big deal. As of now, the rod seems to indicate something like the trusting and loving bond that exists between Joe and his dad. After all, you don't let just anybody go off with your most prized possession.
Of course, we know what ends up happening to the rod: Joe calls what happened "the terrible thing" (9.7). Melodramatic? Maybe... if it were just a stupid fishing rod. But what makes it terrible is that Joe initially thought that he was the one deciding to gain a little independence; as it turns out, he doesn't even have a choice in the matter, because the symbol of independence is taken from him.
Think of what Joe says towards the end of the chapter: "He and his father had lost everything. Themselves and the rod" (9.21). What leads Joe to this conclusion?
Well, the problem is that even though the fishing rod is probably mass-produced, and even though Joe's dad could theoretically just go out and buy another one, the guy just doesn't have enough money to do it: "[N]ow that it was gone he wouldn't have enough money to buy another and so he was a failure" (9.17).
Well, that escalated quickly. The fact that Joe's father can't afford another fishing rod causes Joe to lose a lot (and we mean a lot) of respect for him. Joe is so enslaved by the idea of success being measured by money that he can't even understand the immense wealth provided, for example, by his father's garden (9.9).
There's a connection between the way Joe measures his father in terms of his income and the way war (and sometimes technology) measures in terms of numbers, not individuals. Trumbo gives us the sense that there's some kind of a connection between these two attitudes, as if think in materialistic terms makes it easier to see war as something legit.
So going back to the line about how Joe and his father have lost everything, what does it mean that they have lost "themselves"? Well, they've lost their relationship, and they've lost respect, and the implication is that they aren't going to gain those things back. So it really is a "terrible thing," isn't it?