I can think of a few reasons.

1. Some peels are not easy to eat, don’t taste good, or are not meant to be eaten. Bananas, for example. The peel is just too hard to eat. Maybe animals eat them with the peeling on, but I also think they don’t taste very good.
2. Pesticides. Some fruits, such as apples, are grown with a lot of pesticides. In Japan, pesticides are used liberally. So when people peel their fruit before eating it, it’s likely because they are trying to avoid eating pesticides. I’m not a nutritionist, so I don’t know if the pesticides get through the peel or how much it helps.
3. Habit. Sometimes, people just do things by habit. We don’t think about why we do everything we do. We just do it.

Happy eating!