This chapter is about exploring the incompatibilities between doing central planning of the economy and running the government as a democracy.
Hayek starts by pointing out that we live in times of increasing individual freedom and this growing freedom is the result of growing prosperity.
But at the same time that this freedom and prosperity are growing, there are also cries for more social justice and more equality in how this increased wealth is spread around. One way of increasing the social justice and equality is through central planning, and this approach has become attractive to progressives (of his time).
The main rub is that democracy is about representing plural views -- it's about allowing free people to express many ideas and through that discovering how to allow these many ideas to co-exist. Central planning, on the other hand, is about organizing the resources of the community to accomplish one set of goals from the many possible. If central planning tries to support a plurality of goals, it's wasting resources, and that's not what central planning wants to be about.
This is why democracy and central planning are like oil and water -- democracy does not micromanage well, but that's the heart of central planning. What democracy can support well is rule of law -- setting up the social parameters for what is OK and not OK, then backing off and letting demand, competition and the free market determine how to reach plural goals efficiently. What central planning supports well is dictatorship and totalitarian thinking -- all the resources of the community, including thinking resources, must be dedicated to the one right way.