somebody explain private law please

I don't understand the idea of private law. In a market anarchist society, do you really have to e.g. write a contract with every other individual where you specify that the other guy cannot harm you without paying a penalty? What is wrong with everybody in a given territory accepting a single common body of laws, and if you don't like the laws, you either try to change them through a commonly agreed legislative process or else you move somewhere else?