A common argument used to justify the legalization of same-sex marriage is the equal protection language of the 14th amendment to the constitution.  As I understand it, the practical upshot is that if marriage to whomever you chose is a fundamental right, then the courts should use strict scrutiny regarding any law that restricts that right.  And in so doing, the state would need to demonstrate a compelling interest of the state for any such restriction.  This goes beyond a rational basis requirement – it must be compelling.  The argument would go something like this:

P1:  Marriage to whomever you choose is a fundamental right of citizens of the United States
P2:  Laws that prohibit same-sex marriage are a violation of this right
C1:  The courts should use strict scrutiny of these laws, and strike them down as a violation of the 14th amendment

The response is that marriage to whomever you choose is not a fundamental right.  If this were the case, marriage restrictions such as age, marriage to cousins (or even siblings), plural marriage, etc. would also violate such a right.  These examples (and others) show that marriage to whomever you please is not an fundamental human right.  This is why rational basis of the legislature should be used rather than strict scrutiny of the courts – because there is no fundamental human rights violation regarding marrying whomever you choose.