There are plenty of non-violent interactions without the state. But there are also plenty of violent interactions both with and without the state. The real stretch beyond the realm of the believable is to assume that there will not be violent interactions without the state. After all, non state violence is something that occurs every minute of every day of every year.
But the daily violence that most people face is clearly reduced by the actions of government, when government chooses to do so. Often government looks the other way. And when that happens there are some people claiming that that violence is the fault of the state. This is a question of the difference between an act of commission and an act of omission. If I know you are going to commit violence, and I do nothing to stop you, do I bear some of the responsibility? Sure. But I'm not the one that committed the violence. As near as I can parse out what some people are saying, the person who got out of the way of the violence gets all the blame and the person who commits the violence gets a pass. This is what Ron Paul does when he says that the government caused the financial crisis.
What people do when they blame private violence on the state is to build a false justification for all the private violence to go on unchecked.
The police aren't any good at stopping all crime, so let's abolish the police, and crime will surely cease.
Seriously, where is the logic in that?
And we are not talking about all the people. Maybe 5%, maybe 10%. But that 5 or 10% is not going to cease to exist because of the state getting out of their way. They will do more and more violence. The fundamental irrationality is to assume that anything can make that minority of predators go away. All that can be done is control and punish them and have the threat to them serious enough to discourage them from trying it.
And that doesn't even take into account the reckless violence as opposed to the deliberate.