It's a quirk of the laws that govern the relationships between the federal government and the states and between the various states themselves that divorces must be recognized across state lines but marriages do not. Divorces are court orders, which means they are products of a judicial process, with two sides, attorneys (usually), and a judge. Marriages are not orders or "final decisions" of any court. They are licenses, grants from the executive arm of the state government (usually a clerk's office). This means that if West Virginia is vehemently opposed to, say, first cousins marrying (which it is), then that state does not have to recognize that first cousins who married in New York (which allows them to) are married. But if those once-married first cousins got divorced, West Virginia would have to recognize the results of the divorce order.
This isn't the only possible interpretation of the law, but it is one shared by many historians and legal scholars.
The source of this state of affairs is the U.S. Constitution's full faith and credit clause. Art IV, Sec. 1 of the Constitution states as follows: "Full faith and credit shall be given in each state to the public acts, records, and judicial proceedings of every other state. And the Congress may by general laws prescribe the manner in which such acts, records, and proceedings shall be proved, and the effect thereof."
Read it again. It sounds contradictory. The first sentence says that the states have to recognize the judgments of other states. But the second sentence says that Congress has the power to regulate how that happens. If the states shall listen to their sister states and Congress may pass laws telling them exactly how to do that, then Congress has the power to come along every once in a while and put a wrench in the free flow of full faith and credit between the states.
As originally written, the clauses were meant to ensure that one state didn't discriminate against the residents of another state. Treating everyone equally was always a basic premise of the American ideal (even if it doesn't always make it into practice) and the Framers were worried that in a new nation where states were the primary sources of government authority, states would have the incentive to look after their own residents at the expense of others. According to James Madison, at least, the second clause was meant to allow Congress to step in to make sure that didn't happen.
The clauses were also necessary to create a fully functional national system out of the old Articles of Confederation, which failed mostly because it had no laws effectively binding states together. A court order, the resolution of a dispute, for example, in one state had to be fully recognized in others lest defendants flee to avoid their responsibilities. Without the privileges and immunities clause, then, states could effectively become safe havens for criminals or scofflaws from a neighboring state.
The principle operation of the full faith and credit clause relates to judgments handed down by the courts. If you successfully sue someone for breach of contract in New Jersey, you may find that your debtor — the loser in the case who now owes you money damages — has property in Pennsylvania. You have to be able to take the New Jersey order to Pennsylvania and have Pennsylvania enforce the judgment on your debtor and his Pennsylvania property. Imagine if that were not the case: you could live in one state and toss all your property and money over the border and then run wild, breaching contracts left and right and the courts could never touch you.
Marriages don't have the same character as those kinds of orders. Perhaps that shouldn't matter: the clause does refer to "records" as well as "judicial proceedings." But for various historical reasons, the default marriage law rule is that a state can refuse to recognize an out-of-state, or alien, marriage if it contradicts that state's public policy. That is not true of court judgments like damage awards and divorce orders.
The result is that we nationalized same-sex divorce before we nationalized same-sex marriage. A public policy that does that is perverse, doing more damage to the institution of marriage than any two men in love ever could.
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Ari Ezra Waldman is the Associate Director of the Institute for Information Law and Policy and a professor at New York Law School and is concurrently getting his PhD at Columbia University in New York City. He is a 2002 graduate of Harvard College and a 2005 graduate of Harvard Law School. Ari writes weekly posts on law and various LGBT issues.