"Counter-cyclical education" is a term coined by David Riesman to describe what he sees as the purpose for school in a democratic society.
In the prototypical democratic society, all organizations and workers for The State work together to stress the same values (life, liberty, pursuit of happiness, earning lots of money, whatever). Even when there are checks and balances, such as between the different branches of the US Government, those still aim at the same purpose (upholding the Constitution and serving the will of the people). The traditional conception of schools has been in line with this, as any examination of what ideologies lurk in your high school history textbooks will show.
What David Riesman, Neil Postman, and many others suggest is that schools should actually be dedicated to stressing values that are not held by the society, or more importantly, creating people who can actively critique the values of the society. Thus, schools should work in opposition to the democracy, trying to create people who can invigorate change and fight stasis. Such ideas have manifested them to various forms in progressive education and inquiry schools.