The ongoing federal shutdown offers a powerful lesson about public schools, and it’s not just that you can’t count on checks from D.C. It is something much more basic: When government makes decisions, it is very often a zero-sum game — either you get what you want or someone else does — and that is a recipe for harmony-shredding conflict.

That our nation is politically polarized is obvious. Indeed, it feels like an entire industry has sprung up to let us know just how torn asunder we are. As a Washington Post headline declared recently, “Shutdown’s roots lie in deeply embedded divisions in America’s politics.”

Alas, this isn’t a new or one-time thing. No, it seems that the more Washington has tried to control, the worse our divisions have gotten. Take the president’s health-care law, arguably the biggest single increase in federal power in decades. It is probably also the most divisive; having caused rage-filled town halls before it was rammed through on a purely partisan vote, it now drives much of the current federal paralysis.

Basically, the more that government does, the more inevitable divisive warfare becomes. Government action forces everyone into the political arena to determine who gets what from whom, rather than letting people freely choose with whom they’ll interact, and freely choose to cooperate for mutual advantage.

Ironically, perhaps the fundamental notion undergirding public schooling is that government control is essential to bind diverse people together. Horace Mann, the “Father of the Common Schools,” declared that the only way Americans could be educated and kept out of “social, interminable warfare … is the elevation of the common schools.”

How has that worked out?

In Mann’s Massachusetts, the common schools first exacerbated long-simmering tensions between Congregationalists and Unitarians — Mann was among the latter — forcing them to debate what kind of religion the schools would teach. It was a burning dispute dampened only by the arrival of large numbers of Roman Catholics — at the time, a common enemy of many Protestants.

Roughly a century of political and social tension between American Catholics and Protestants is well documented. But the battles were perhaps most heated in education, where they included physical combat — with numerous people killed — in the 1844 “Philadelphia Bible Riots.” The spark that set off the conflagration was the question of whose version, if any, of the Bible would be used in the public schools.

Of course, numerous districts for many decades saw peace. What largely maintained tranquility was that, unlike Philadelphia and other diverse areas, most districts were small and their communities homogeneous. That, and large “out” groups — especially African Americans — either were shamefully barred from public schools or, in the case of Roman Catholics, established their own institutions.

As public schooling evolved, it became increasingly centralized, first with consolidated districts, then with state and federal controls. With extremely diverse people now placed under unified governance, today we see constant conflict over numerous values-laden, intensely personal matters, including religion in the schools (or lack thereof); portrayals of different races and ethnicities in curricula and texts; student speech rights; reading selections; and the list goes on.

Indeed, the Cato Institute has been tracking public-schooling battles since 2007 and has posted a map (with ongoing updates) identifying hundreds of “values” battles across the country. And those are just the throwdowns that have received relatively prominent media attention.

Painfully illustrative of the problem is the Anoka-Hennepin district in Minnesota, north of Minneapolis. First it was torn by accusations, in the wake of several student suicides, that it fostered an environment hostile to gay students. Then it came under fire for contemplating policies that conservatives considered threats to their values. Superintendent Dennis Carlson concluded that being a district designed to incorporate very diverse people was the root cause of the seemingly inescapable conflict. Then he said, “It’s not a battle we want to fight. That’s not why we’re here.”

Sadly, Mr. Carlson is wrong: Forcing diverse people together is why public schools are here, as Horace Mann himself proclaimed. But as we are learning the hard way, not just in education but across politics, government control often does not yield harmony. Indeed, quite the opposite.