I think they summarise their arguments themselves. For example
"Although the policy arguments for extending marriage to same-sex couples may be compelling, the legal arguments for requiring such an extension are not. The fundamental right to marry does not include a right to make a State change its definition of marriage. And a State’s decision to maintain the meaning of marriage that has persisted in every culture throughout human history can hardly be called irrational. In short, our Constitution does not enact any one theory of marriage. The people of a State are free to expand marriage to include same-sex couples, or to retain the historic definition."
There are plenty of other examples of far more extreme behavior that was tolerated. So saying a Roman Emperor was unable to marry is clearly wrong ex: Nero.
"Although the policy arguments for extending marriage to same-sex couples may be compelling, the legal arguments for requiring such an extension are not. The fundamental right to marry does not include a right to make a State change its definition of marriage. And a State’s decision to maintain the meaning of marriage that has persisted in every culture throughout human history can hardly be called irrational. In short, our Constitution does not enact any one theory of marriage. The people of a State are free to expand marriage to include same-sex couples, or to retain the historic definition."
[p. 2 of Robert's opinion, p. 41 of the pdf] http://www.supremecourt.gov/opinions/14pdf/14-556_3204.pdf