> States have a monopoly on violence

This could be amended to "States have a monopoly legitimate on violence". Your comment seems to deny the existence of "legitimacy" as a concept. How do you distinguish between legitimate and illegitimate use of force?

No, states can't do violence because they don't have hands, so they can't hold guns or bats. The violence is done on behalf of the state by some of the people it convinces, mostly police officers and soldiers.