Why must private property rights be publicly provided?

I have been thinking about this question for a while now. Most political economic theory takes it for granted that property rights have to be created and enforced by a government, and I certainly agree, but I have not heard a clear and concrete theory for why private action will not create a system of property rights. It seems intuitively obvious, but it is difficult to come up with a clear explanation. What is the market failure?

Does anyone have an explanation? Has someone explained this before?