How did Obergefell v. Hodges legalize same-sex marriage throughout the United States?

In the 2015 landmark case Obergefell v. Hodges, the U.S. Supreme Court ruled in a 5–4 decision that state-level bans on same-sex marriage and the refusal to recognize such marriages performed in other jurisdictions were unconstitutional.1

The Court’s majority opinion, written by Justice Anthony Kennedy, established that the right to marry is a fundamental right inherent in the liberty of the person, protected by the due process clause of the Fourteenth Amendment. Furthermore, the Court held that the equal protection clause of the same amendment prohibits states from denying same-sex couples the equal protection of the laws.1

By affirming that the reasons marriage is considered a fundamental right apply with equal force to same-sex couples, the ruling effectively invalidated all state laws and constitutional amendments that defined marriage exclusively as a union between a man and a woman, thereby legalizing same-sex marriage across all 50 states.12