From the opinion, p2.
"(b) The Fourteenth Amendment requires a State to license a marriage
between two people of the same sex. Pp. 10–27.
(1) The fundamental liberties protected by the Fourteenth
Amendment’s Due Process Clause extend to certain personal choices
central to individual dignity and autonomy, including intimate choices
defining personal identity and beliefs. See, e.g., Eisenstadt v.
Baird, 405 U. S. 438, 453; Griswold v. Connecticut, 381 U. S. 479,
484–486. Courts must exercise reasoned judgment in identifying interests
of the person so fundamental that the State must accord them
its respect. History and tradition guide and discipline the inquiry
but do not set its outer boundaries. When new insight reveals discord
between the Constitution’s central protections and a received legal
stricture, a claim to liberty must be addressed.
Applying these tenets, the Court has long held the right to marry is
protected by the Constitution. For example, Loving v. Virginia, 388
U. S. 1, 12, invalidated bans on interracial unions, and Turner v.
Safley, 482 U. S. 78, 95, held that prisoners could not be denied the
right to marry."
Seems like they get right to the heart of the legal matter and reasoning, despite what some here may claim.