Being able to developer a personality, your personality, yourself basically.
IMHO Shoshana Zuboff explores this quite well. Imagine all the time there was an entity who was able to watch over everything you do, all the time, and could act on it, either by telling your government or companies, would you truly do everything you want to do? Note that this doesn’t mean anything illegal or immoral, especially as a young person when one does not even know what that means. I also would link that to the chilling effect, for example if one does truly believe Google or Facebook can know a lot about you and if say you want to reach a position of power, say become a politician, would you dare criticize them knowing they might give information to your opponent?
So… IMHO some of the perceivable benefit of being private is that you can become an individual, not a transparent clone of what some commercial actors of society today expect you to be. That is particularly important in a democracy where we collectively decide what is right or wrong and how we define our own future.