I think it goes even deeper than that. I firmly believe in my own right to privacy, but as an adult, I also have some understanding of the consequences and implications of my actions, and this informs what I do, and what I share.
Children do not and cannot have this luxury. They should not be held responsible for their choices and actions in the way that adults are, and a part of this is ensuring that their life is not documented with the level of permanency that is inherent in the internet.