From the 14th Amendment, Section 1:

"No state shall make or enforce any law which shall abridge the privileges or immunities of citizens of the United States; nor shall any state deprive any person of life, liberty, or property, without due process of law; nor deny to any person within its jurisdiction the equal protection of the laws."

The 14th Amendment has two Applicable Parts: The Due Process Clause and the Equal Protection Clause:

Under the Due Process Clause, no state can deprive its citizens of life, liberty or property (which has been interpreted to include rights and freedoms) without due process of law. This means states cannot deprive their citizens of rights contained in, guaranteed by or extending from the U.S. Constitution. Although the US Constitution does not mention marriage in any way, it does contain a "Full Faith and Credit Clause" which requires state A to honor contracts made in state B. This is also applied to things such as license plates, legal name changes, car registrations, divorces, adoptions and marriages. The 1996 Defense of Marriage Act ("DOMA") purports to enable states to violate the Full Faith and Credit Clause with respect to marriage, based upon the gender of the parties thereto. One can argue that the Due Process Clause prohibits states from violating the Full Faith and Credit Clause without judicial review.Under the Equal Protection Clause, a state must provide equal protection under the law to all persons within its jurisdiction. This means that if a state enacts a law that has an adverse impact on one group of people, it may not do so arbitrarily and there must exist a compelling need for the law to be enacted.As evidenced by California's Proposition 8 trials, it can be difficult to come up with a legal argument against same-sex marriage without relying upon religious doctrine which is inadmissible. This is one reason why the parties who sued to prevent same-sex marriage in California also fought very hard to prevent videotape of them speaking the arguments they made in court from being released to the public. They themselves argued that if the public saw them saying the things they said in Court, there would be outrage, death threats and their careers would be irreparably harmed. One can argue that the Equal Protection Clause is violated by states that permit some citizens to marry, but not others and then cannot produce a coherent argument as to why this is necessary.