In a Jewish mindset, the Rod is what one has that symbolizes authority. Like the head of a tribe, a clan, or a household. It's a walking implement and something to ward off predators. Think of it like a
Bo staff.
They'd not be using that on their kids or adult children. It's a tree branch!
Shepherds don't whip their sheep with their staff. They ward off predators and thieves.
Punitive, physical punishment is very, very frowned upon in the Jewish community.