With friendship, there are two people involved. One person can't demand the friendship be private if the other disagrees. If one person makes it public, it's public. It works that way in real life too.
"Tell you what, we both go to the same summer camp, so we can be camp friends. But if I see you at school, I won't admit that we are friends. If you try to bring it up, I'll deny it."
Facebook is always biased towards sharing information, instead of respecting privacy. They also apparently don't have the technical ability to keep private things private, as shown by the multiple leaks of Zuckerberg's information. When was the last time that Larry Page's gmail was hacked?
In any case, I disagree with your point. I think if either party makes the friendship private, it should be private.
Your example seems contrived. I didn't have friends as a kid, so I don't really know, but that seems like an unusual arrangement. At the very least, it requires you to do it explicitly.
Usually, in real life, if one person wants a friendship to be private while the other one wants it to be public, they don't stay friends for very long.
...but if I have a friendship with you that I want to remain private for some reason, and you make it public, you are going against my wishes, you are a bad person, and you shouldn't do that.
This can often result in injury or death to the person who typically has a good reason for keeping their relationship secret.
I have a friend who is dating two women, neither of which who knows about the existence of the other. If he was to tell each woman, please update your Facebook privacy settings to keep our friendship a secret, they would rightly be suspicious. If them finding out about each other results in injury or death to him, it's not Facebook's fault.
