The anti-prop 8 side argued, for the most part, that the court should not allow a restriction on a fundamendal right (i.e. marriage) with respect to a minority group to occur through the simple amendment process like prop 8 went through (i.e. simply getting a majority vote on a proposition).  Instead, at minimum, it should require the more onerous revision process (which requires approval by the legislature and a statewide vote).

Thus, the State contends that, because its miscegenation statutes punish equally both the white and the Negro participants in an interracial marriage, these statutes, despite their reliance on racial classifications, do not constitute an invidious discrimination based upon race....

There is patently no legitimate overriding purpose independent of invidious racial discrimination which justifies this classification. The fact that Virginia prohibits only interracial marriages involving white persons demonstrates that the racial classifications must stand on their own justification, as measures designed to maintain White Supremacy.  We have consistently denied the constitutionality of measures which restrict the rights of citizens on account of race. There can be no doubt that restricting the freedom to marry solely because of racial classifications violates the central meaning of the Equal Protection Clause.