Those who prefer the under position have equally interesting reasons. Some believe it creates a cleaner appearance because the loose end stays closer to the wall. Others find it more convenient with particular toilet-paper holders. The arrangement can also be useful for people who own curious cats that enjoy pulling hanging paper until the entire roll unravels across the bathroom floor.
For these households, placing the loose end underneath may reduce the temptation for playful pets. It is not guaranteed to prevent every mess, but it can make grabbing the paper less convenient for curious animals. Clearly, the best arrangement can depend on the household.