Facebook needs to introduce a way to delete both sides of a conversation when requested by someone who feels uncomfortable or threatened in any way by having that conversation remain in print.

These conversations might contain personal and sensitive data like telephone numbers, password to devices and services, credit card informations or just confessions about our problems. Someone may regret to have confided these informations to people that don't trust anymore and would like to permanently delete those conversations on both sides. Of course the "receiver" might have copied them somewhere else (and you can't do anything about it) but
people MUST HAVE THE RIGHT to do what they want with their own conversations.

Spoken words get forgotten while written ones don't. That's why they must be deleted.