Some brief arguments on behalf of traditional marriage:
Conservatives hold a deep respect for tradition. Every generation possesses a cultural inheritance bestowed to them by earlier generations. Whatever traditions constitute part of this inheritance rest upon the reasoning of those earlier generations. Traditions can be changed; some should be changed. Conservatives hold that tradition remains the default position, however, and that suggested changes must have compelling reasons as justification.
Traditional marriage between one man and one women is such tradition. (It is, of course, a Western European tradition as part of our cultural inheritance from the Greeks and the Romans. It is NOT a biblical tradition, although Christianity has sanctioned traditional marriage. Biblical marriage, of course, is polygamous.)
Traditional marriage is a social reality based upon biological reality. Men and women engage in sexual intercourse, procreate, rear their offspring, and form kinship networks based upon consanguinity. Homosexual couples cannot do these things. They cannot engage in sexual intercourse properly speaking. They cannot procreate. They cannot form new kinship networks based upon consanguinity.
Obviously, some marriage couples cannot procreate. Although evolution designed two genders for the continued preservation of the species, some people are unable to have children. The fact that some couples cannot have children or that some couples choose not to have children seems irrelevant to the question of same sex marriage. Marriage recognizes the potentiality for children. No same sex couple possesses the potentiality for children.
Centuries ago, Aristotle argued that to understand the justice of any social practice, one must understand its telos--its end or purpose. Only traditional marriage fulfills the fundamental purposes of family formation. Consequently, it is just to restrict marriage to the traditional formula of one man and one woman.
And this is why in every state the laws defining marriage as a union between one man and one woman constitute part of family law or family code.
Marriage is a social convention with social purposes that we as a society can change and define anyway we want. We can change the definition of marriage to include couples of the same sex. We change the definition of marriage to include good old fashioned Biblical or Koranic polygamy. We can change the definition to include new fashioned gender neutral polyamorous relationships.
There just do not seem to be any compelling reasons why we should.