I’ve always stressed that passwords should never be shared with anyone, to everyone I discuss them with — the only passwords that my wife and I both know are the ones to the iTunes and e-book accounts that we both share.
Unfortunately there’s a problem when it comes to minors: parents only have a limited amount of trust in their kids, usually with reason, and insist on knowing their childrens’ passwords. It sounds like that’s leading to a problem: kids think that sharing a password with a boyfriend/girlfriend is an appropriate way to show trust in them, with some consequences that are pretty obvious to anyone who has lived through their own teenage breakups.
There’s a solution: accounts for children could have a second, and separate, password for their parents. Then the kids learn good password habits and the parents can still check up on them if they feel the need. It’s even something of an improvement, since the kids can’t change the password to one the parents don’t know, and parents could presumably fix forgotten passwords for them. Of course, that opens up a whole ‘nuther set of problems (password management for the sites and programs using it, how does the site make sure the parent is the one setting the parental password and not the kid, and the big one, the fact that it’s a change from the way things are — just to name a few obvious ones), but those could be dealt with, if the will existed. Meaning they won’t be dealt with, and kids will continue to share their passwords, with predictable consequences.