You don't have to eat them. There's no benefit to eating them. They don't taste good. They provide a negligible amount of nutrition, if any, and harm you very mildly. The stem of an apple is edible, but for what? A gram of extra fiber after you manage to gnaw through it?
You can eat banana peels, but you probably wouldn't want to. It's a terrible texture and flavor. They decompose well, so there's no meaningful environmental benefit. Yes, they have nutrients. You can eat a second piece of fruit instead.
And this is not universally good advice. The seeds, leaves, and stem of the pawpaw is filled with toxins—enough that folks have died from it.
I don't think the author is trying to make a point, but rather to show that we do things because we were told them. But it's important to also realize that the cultural reasons are sometimes backed up with hard-earned lessons or to save us from having to learn for ourselves that watermelon rind isn't pleasant to eat without preparing it in other ways.