In the craziness of the two and a half hours of oral argument last week concerning whether the Constitution requires states to recognize same-sex relationships as marriages, it’s understandable that some errors were made. With the luxury and wisdom of hindsight, this essay corrects those errors.

Error Number One: Massachusetts Marriage Rates Have Stayed the Same

During the questioning of Michigan’s attorney, John Bursch, Justice Sotomayor commented that “In Massachusetts, we’ve got data that it’s—the rates have remained constant since they changed their laws.” Unfortunately, Mr. Bursch did not correct her error.

Justice Sotomayor is only correct if Massachusetts includes same-sex marriages in that number. But that’s not helpful, since the argument being made is that redefining the institution of marriage will, in the long run, lower the opposite-sex marriage rate. In Justice Sotomayor’s defense, she is probably relying on the amicus brief filed by Massachusetts and other states where they deceptively report overall marriage rates—which include the new addition of same-sex marriages—and claim there has been no decrease in marriage rates since the state adopted same-sex marriage.

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But what Justice Sotomayor missed is an opposing amicus brief filed by 100 Scholars of Marriage that actually obtained data from the state of Massachusetts on opposite-sex marriage rates since 2003 (the year before the state adopted same-sex marriage). Those data—the only relevant data here—paint a different picture. Opposite-sex marriage rates have dropped by 8.9 percent since the state redefined marriage.

And Massachusetts is not alone. The marriage scholars were also able to obtain data on opposite-sex marriage rates from three other states that have legalized same-sex marriage, and they likewise have seen declines: Vermont (-5.1 percent), Connecticut (-7.3 percent), and Iowa (-9.2 percent). Other states have not had same-sex marriage long enough for data to be reported, since there is usually a lag of a couple of years before data are available.

Of course, correlation does not prove causation. But Justice Sotomayor was wrong: opposite-sex marriage rates have declined in Massachusetts since the legalization of same-sex marriage.

Error Number Two: Because Some Men Leave Their Wives and Children, Marriage Does Not Help Keep Fathers Around

Justice Sotomayor also committed what is commonly referred to as an exception fallacy. This is where someone reaches an overall conclusion about a group on the basis of a few exceptional cases. Thus, when Mr. Bursch was making the argument that redefining marriage to include same-sex couples will disconnect marriage from the long-held norm that the institution binds children to their biological mother and father, Justice Sotomayor responded:

Marriage doesn’t do that on any level. How many married couples do fathers with the benefits or the requirements of marriage walk away from their children? So it’s not that the institution alone does it and that without it that father is going to stay in marriage. He made a choice . . . Some mothers do the same thing.

This is a classic example of the exception fallacy. Of course some men and women walk away from their marriage and their children. But that is the exception, not the rule, and it is certainly counter to the social norm of marriage that gently pushes parents to stay together and raise their children.

It is rather shocking that a justice of the United States Supreme Court would claim that “on any level” marriage does not have that effect and longstanding purpose. It is also disappointing that she would commit such a basic error of logic.

Error Number Three: The Purpose of States’ Recognizing and Regulating Marriage is to Bestow Dignity on Couples

Justice Kennedy expressed surprise when Mr. Bursch argued that the states are not in the marriage business to bestow dignity. Justice Kennedy responded:

I don’t understand this is not dignity bestowing. I thought that was the whole purpose of marriage. It bestows dignity on both man and woman in a traditional marriage. It’s dignity bestowing, and these parties say they want to have that—that same ennoblement. Or am I missing your point?

Yes, Justice Kennedy was missing the point. He was confusing the reason that a couple may desire to be married with the reason that a state would want to recognize and regulate marriage. Those are distinct.

Take a driver’s license, for example. Why would a sixteen-year-old want to get a driver’s license? To be like his or her peers, to be accepted or cool, or at least not be an oddball. A teenager will also want to feel more grown up and to have more freedom. But why does the state grant driver’s licenses to teenagers? It’s not so that sixteen-year-olds feel better about themselves, or feel more accepted by their peers, or feel more like an adult, or have more freedom. States hand out driver’s licenses to teenagers (after the requisite driver’s education courses and driving tests) to regulate who can drive cars in the interest of keeping the roads safe for all citizens.

The same goes for marriage. Couples and states do not have the same purposes.

Justice Kennedy was also possibly confusing means with ends. Even assuming, for the sake of argument, that states were interested in bestowing dignity on couples by allowing them to marry, that would be a means to enticing couples to marry. The end or purpose of encouraging marriage in this way would still be the fact that society—particularly children—benefits when men and women marry. It makes no sense for the state to go through the trouble and expense to regulate and subsidize marriage if the state gets nothing out of it in return—and it’s not simply about bestowing dignity on consenting adult love of all sizes and shapes.

Further, Justice Kennedy’s conception of state motivations for granting the right to marry to couples is most likely unconstitutional under his own jurisprudence. If a state is only allowing couples to marry in order to bestow dignity upon them—with the state getting no benefits in return—then either the state has no rational basis for granting marriage rights, or the state is acting out of animus toward the unmarried, or toward other, non-marital, forms of consenting adult romantic relationships. For if the state has no rational basis for believing that a law would provide a tangible benefit, then privileging one group over the other would violate the Constitution according to Justice Kennedy’s own opinions.

Thus, as a matter of fact, of logic, and of constitutional analysis, Justice Kennedy is wrong.

Error Number Four: The Only Harm to Legalizing Same-Sex Marriage Is Making Marriage More Adult-Centered

Several justices struggled to see how redefining marriage in genderless terms would cause any harm or have any impact on the institution of marriage. As Mr. Bursch correctly but incompletely argued, legalizing same-sex marriage will alter the institution to be primarily concerned with fulfilling the desires of adults rather than the needs of children.

But that’s not all. As the 100 Scholars of Marriage made clear in their amicus brief, several other important and beneficial social norms will be eroded, if not erased, by same-sex marriage, including:

– Gender-diverse parenting: the norm that children both need and deserve to be raised by a man and a woman, not only because of what they learn from interacting with a parent of each sex, but because men and women parent and interact with their children differently, providing distinct but complementary benefits. By its very structure, same-sex marriage eliminates this norm and its attendant benefits to children.

– Biological bonding: the norm that marriage binds children to their biological mother and father in a family unit. Same-sex marriage and parenting, by definition, means that at best only one of a child’s biological parents will be in the home. While death, divorce, or parental delinquency create exceptions, elevating the exception to the norm undermines that norm and the benefits it produces.

– Postponing or channeling procreation: the norm that procreation should only responsibly occur within the stable bonds of marriage. Same-sex marriage is not, and biologically cannot be, about procreation. By redefining marriage in this way, the institution becomes less about being the socially recommended “place” and “time” where procreation is recommended.

– Placing social value on raising children: the norm that society values and needs children to be born and raised by their parents. Again, same-sex marriage is not primarily about procreation, and its acceptance attenuates this norm for the institution as a whole. Of course, same-sex couples can adopt or one member of the couple can reproduce with someone of the opposite sex, but these are secondary purposes and behaviors.

What impact will the weakening or elimination of these norms have on the institution of marriage, and thus the behavior of society? Put another way, as Justice Breyer asked, “what’s the empirical connection?”

Well, the last major alteration to the institution of marriage—no-fault divorce—did have unintended negative consequences, reducing marriage rates and increasing divorce rates more than expected, with children and women suffering the consequences. Additionally, the Netherlands, the country that has had same-sex marriage the longest, after controlling for other factors, has experienced a drop in opposite-sex marriage rates among young women after adopting same-sex marriage.

The truth is, no one knows for sure what the effect will be—but it clashes with history, common sense, and theory to assume it will be innocuous.

Error Number Five: There Is a Parallel between Brown/Loving and Lawrence/Obergefell

The time between the Supreme Court decision calling for desegregation of elementary schools, the famous Brown v. Board of Education, and the decision invalidating state laws that prohibited mixed-race marriages (Loving v. Virginia), was thirteen years. Similarly, the time between the Supreme Court decision striking down laws criminalizing homosexual sodomy (Lawrence v. Texas) and today is also thirteen years.

Twice during oral argument Justice Kennedy, almost thinking aloud, noted those two time frames were equivalent. He thus implied that it was time to constitutionalize a right to same-sex marriage.

But while the number of years may be the same, the time is not really equivalent. Even Justice Kennedy seemed to hint at that. If one thinks of the thirteen years as the numerator in a fraction, the denominator is remarkably different in these two instances. At the time of Loving, state prohibitions on inter-racial marriages had been in existence in only some of the states, and then at most for about 300 years if we go back to colonial times in Virginia and Maryland.

But man-woman marriage has been the law in every state since the birth of the nation—and in every Western nation for millennia. As Justice Kennedy put it, “I don’t even know how to count the decimals when we talk about millennia.”

Not all thirteen year periods are equivalent. They certainly are not here.

Error Number Six: Age Restrictions on Marriage Are Equivalent to the Definitional Element of One Man and One Woman

While debating whether states should be required to recognize same-sex marriages performed in other states, the issue of age restrictions arose. Despite states’ varying age restrictions, it is rare for a state not to recognize a valid out-of-state marriage between a man and a woman, even if one or both of the spouses are too young to legally marry in that state.

Several of the justices questioned whether there was a difference between recognizing exceptions to age restrictions and recognizing same-sex marriages.

In short: yes, there is. Not all exceptions are equal. Age has never been a part of the definition of marriage. That is evident from the fact that there was such variation on which age should be the legal cutoff. There are two historical and universal components to the definition of marriage in the United States, and in the Western world: gender diversity and only two spouses, one man and one woman. All other features—age, race, religion, coverture, dowry—are not part of the fundamental definition and thus vary, if and when they are found in marriage law.

Thus, the difference between age restrictions and defining marriage as only between one man and one woman is the difference between degree and kind. The definition of marriage is unchanged by the fact that a spouse is seventeen rather than nineteen. But marriage has been redefined if it is not between a man and a woman.

Ideally, oral arguments clarify the issues at stake in a particular case. Unfortunately, they sometimes perpetuate errors instead—in this instance, at least six. Whichever way the Supreme Court ultimately decides, it should do so based on fact and truth, not error and fallacy.

Surely the people and the Constitution deserve as much.