This is a chapter about freedom. It stresses that freedom to the individual comes from economic competition -- that both monopoly and planning are the enemies of personal freedom. The freedom comes from the freedom to make choices in both what the person consumes and what the person produces (their job). A person is not free if a monopolist or a government controls those choices.
Hayek points out that the world is full of luck. The difference is whether this luck is due to impartial forces, as it is in a competitive environment, or due to the choices of an official with coercive power, as it is in the planned environment.
He points out that one of the deepest weaknesses in the various socialist systems is that defining the "more equal distribution system" -- the admirable social justice goal of all socialist systems -- has no single clear answer. Because there are many popular definitions, just who makes it to the top of the command chain will determine which of the many choices is right, and that choice can be frequently modified when pressured by expedience, and ultimately will be decided by the coercive force available to the planners.
Because there is just one right answer (at a time), indoctrination becomes a necessary tool for planners. It communicates to the group members what the planners have decided the right choice is. He also points out that it was various earlier socialist groups, not Nazis or Fascists, who first developed indoctrinating tools such as organized sports activities for workers, youths and children.
Hayek points out that a big difference between older socialist groups and Nazis and Fascists is who is being appealed to. The older socialists appealed to the rising class of well-paid, skilled industrial workers who were demanding more from their monopolist employers and getting it. The Nazis and Fascist experienced their explosive growth in popularity by appealing to a different group -- the parts of the middle class that weren't industrial workers, such as clerks, salary workers, and teachers -- who were not seeing any benefits in the more equal distribution systems that the older socialist groups were advocating.