Any act of violence -- even in self-defense -- has ramifications for everyone in the community. If X threatens violence against Y, there is probable cause to believe X might also be a violent threat to Z as well -- a violent threat to everyone else. Violence is inherently a public matter, inherently an externality; it cannot properly be privatized and, to use an economics term, the costs of it cannot be fully "internalized." By that I mean that if X hits Y,and then Y hits X back, it doesn't mean that Y's retaliation has made them both even. Y's "private" retaliation does not render this a private matter that can be dropped. No, this remains a public matter because the violence can still escalate.
Anyone who uses violence -- even in self-defense -- is a possible threat to everyone else, and that is why, even when someone uses violence in self-defense, it is right for police and courts to look into the matter and ascertain whether it was indeed self-defense.
And serious threats of violence -- even if not yet acted upon -- are worthy of police attention, as they create probable cause for members of the community to ascertain that the violent threat might be acted upon. Moreover, if Q goes around falsely accusing R of making a violent threat toward Q, that counts as an initiation of the use of force, as third parties, mistakenly believing they are exercising retaliatory force in defense of Q, may end up being violent toward R, and this would end up being an initiation of the use of force.
Violence and the threat of it are the greatest threat to anyone's liberty; violent threats are what deny someone the freedom of peaceful action. Moreover, a right to privacy does not extend to someone threatening violence. That is, if L seriously threatens violence against her own mother, that is something the public has a right to know about, even if L's mother herself tries to dismiss that as something not to be taken seriously. Even if L's mother dismisses it, other people around L remain potential victims of L if L does not receive proper treatment from mental health professionals or the law.
If you have been threatened with violence, or if it has already been inflicted upon you, you may be justified in fearing that if you come forward to authorities with this information, that it may put you at risk of being subjected to violent reprisals from the assailant. For that reason, in the short term it may be rational that you tell but a few people about this circumstance and ask them to keep it secret in the foreseeable future. However, that can only go so far. There is probable cause for the law to inquire as to whether this alleged assailant may pose a violent threat to parties besides you and therefore, in the long run, the protection of every peaceful person's rights requires that this information ultimately be publicly available. On that basis, a right to privacy does not extend to any credible accusation that you can level about someone either threatening violence or having committed it.
