Ironically, it is this socialist system that is primarily responsible for the widespread belief among non-libertarians that "the United States has never been a socialist country," as New York Times columnist Timothy Egan stated in a recent NYT op-ed. (See my two recent articles "A Life of the Lie on Socialism" and "Socialism in America, 31 Years Ago.")
It is worth noting that public schooling is a core feature of the educational systems in Cuba, North Korea, and Vietnam, all three of which are widely known as socialist countries. That's because public schooling is a socialist system.
Perhaps it's also worth noting that while we call it "public" schooling, a more accurate name for it is government schooling or state schooling. That's because state and local governments own and operate the educational systems. If state and local governments owned and operated churches, would we call them public churches or state churches?