The responsibilities and duties one has to their child vs an adult are quite different. Virtually every authority charged with last-resort solving interpersonal conflict issues (government) uses violence, as when all else fails some at least respond to that.

The reason why corporal punishment isn't used privately man to man is because we've delegated that to government, who happily sends men with guns to drag people violently in for reform. Spanking a child before they get to that point would be a favor.