The institution of marriage stands for sexual relations, companionship, love, child-rearing and shared responsibility. Because same-sex relationships do not support the fundamental institutions of marriage.
We allow impotence, a lack of enthusiasm for sex and one party’s reluctance to rear children as grounds for divorce because they are the antithesis to the marital institution. Therefore, it makes sense that we deny marriage licenses to those that do not buy into that institution. Same-sex couples cannot rear children. Therefore, they cannot buy into a key component of the institution of marriage. 
If we accept that sexual relations, companionship, love, child-rearing, and shared responsibility are the pillars of marriage, and we reject any legal unions that do not aspire to uphold the marital institution, then along with homosexual relationships, we would have to exclude asexual relationships, relationships between couples with no child-rearing aspirations, and relationships between couples with no capacity for love from the marital institution. Also, there is no reason why a same-sex couple cannot support all of these institutional pillars. Same-sex couples can and do rear children in a loving environment. Finally, the notion that all of these components are prerequisites for marriage is debatable. Marriage means different things to different people. For some, it may mean love, for others deep understanding. For some, sexual relations are a key component of marriage, for others, they are absent. The definition of what marriage means to that specific couple should have no influence on their legal ability to wed. 
[P1] Childrearing is a key pillar of the marital institution. [P2] Gay couples cannot procreate. [P3] Therefore, a gay relationship is not compatible with the institution of marriage.
Rejecting the premises
[Rejecting P1] Childrearing is not a part of the marital institution. [Rejecting P2] Gay couples can rear children. [Rejecting P3] Gay relationships are compatible with all of the pillars of marriage.