Liability Insurance vs. Full Coverage?

Can someone explain to me why I would need full coverage insurance on a vehicle I have paid off? As I understand it, I would have no insurance coverage for myself if I was harmed or for my vehicle. I don’t care about the vehicle so much, and I don’t see why I would need insurance for myself when I have great medical insurance. Someone please explain! This is confusing me, and I want to make the right choice on how to lower my insurance now that I have paid my vehicle loan off.