Traditionally, marriage and procreation have been tightly connected to one another. Indeed, from a sociological perspective, the primary purpose that marriage serves is to secure a mother and father for each child who is born into a society. Now, however, many Westerners see marriage in primarily emotional terms.
Among other things, the danger with this mentality is that it fosters an anti-natalist mindset that fuels population decline, which in turn puts tremendous social, political, and economic strains on the larger society. Same-sex marriage would only further undercut the procreative norm long associated with marriage insofar as it establishes that there is no necessary link between procreation and marriage.
This was spelled out in the Goodridge decision in Massachusetts, where the majority opinion dismissed the procreative meaning of marriage. It is no accident that the countries that have legalized or are considering legalizing same-sex marriage have some of the lowest fertility rates in the world. For instance, the Netherlands, Sweden, and Canada have birthrates that hover around 1.6 children per woman--well below the replacement fertility rate of 2.1