For children, education is an issue between their parents and the instructors they choose for them. For adults, education is a matter between student and teacher.
Education is never the business of government; brainwashing is the business of government.
All tax-funded education falls under the definition of brainwashing because taxation is coercion.
Voluntary education is not brainwashing because, by definition, it doesn't involve coercion.
Contrary to the coercive public education monopoly (where are those "Trust Busters" when you need them?) banishing government from all classrooms would cause opportunities for education to explode.