Because Burnham's neoconservatism is a sort of fusion of Marxist vanguardism and Walter Lippmann's panels of experts making decisions for the Phantom Public and selling them with lies. Burnham thought that the only possible way to maintain a civilization was through a small group of executive elites with access to the truth, but who kept the mass of the ignorant public docile through patriotic myths and slogans, and policing.

There's no possible stable order for Burnham within a society that is not run by a minority in its own interest.