This is the gist of the Majority's reasoning:
"The nature of injustice is that we may not always see it in our own times. The generations that wrote and ratified the Bill of Rights and the Fourteenth Amendment did not presume to know the extent of freedom in all of its dimensions, and so they entrusted to future generations a charter protecting the right of all persons to enjoy liberty as we learn its meaning. When new insight reveals discord between the Constitution’s central protections and a received legal stricture, a claim to liberty must be addressed.
The limitation of marriage to opposite-sex couples may long have seemed natural and just, but its inconsistency with the central meaning of the fundamental right to marry is now manifest. With that knowledge must come the recognition that laws excluding same-sex couples from the marriage right impose stigma and injury of the kind prohibited by our basic charter."
"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.
If you are among the many Americans—of whatever sexual orientation—who favor expanding same-sex marriage, by all means celebrate today’s decision. Celebrate the achievement of a desired goal. Celebrate the opportunity for a new expression of commitment to a partner. Celebrate the availability of new benefits. But do not celebrate the Constitution. It had nothing to do with it."
"If, even as the price to be paid for a fifth vote, I ever joined an opinion for the Court that began: 'The Constitution promises liberty to all within its reach, a liberty that includes certain specific rights that allow persons, within a lawful realm, to define and express their identity,' I would hide my head in a bag. The Supreme Court of the United States has descended from the disciplined legal reasoning of John Marshall and Joseph Story to the mystical aphorisms of the fortune cookie."
Thomas and Alito's dissents are predictable and reasonable, but not as quotable as the others.
I am incredibly happy with the on-the-ground result of this decision. Denying marriage to same-sex couples is wrong. But legally speaking, I agree with Roberts' dissent. I worry about what might happen when an issue comes up in which my personal policy preferences are inconsistent with those of 5 justices on the Supreme Court.