The rule of two
The rule of opposites
The rule of sex
The three rules go together. A man and a woman are drawn to one another, the natural result of which is that they wish to have sex with one another, the natural result of which is a child. Marriage is a social institution created to provide that child with his or her own mother and father permanently. Marriage also makes the sex between the man and woman legitimate, because it protects them from the natural shocks that any human relationship is subject too, and pre-emptively protects any future children that could normally be expected to result from their sexual relationship.
Blankenhorn thinks an assault on any one of these rules would lead to undermining them all. For this reason, he opposes same-sex marriage. He does not object to homosexuals, homosexuality, or, as far as I can tell, homosexual sex. His concern, rather, is to protect children. He views marriage as the greatest social invention to protect children. Any social move that deinstitutionalizes marriage will soon hurt all kids some, and hurt some kids terribly.
Blankenhorn details well that there is a concerted effort to deinstitutionalize marriage. He takes Judith Stacey as a leader in this movement, and refers to the extreme position that she represents as "the Full Stacey." Stacey is against all three rules of marriage, and openly wants to deinstitutionalize marriage altogether. Her position is that any relationship, made by any number or composition of consenting adults, constitutes a marriage if they say so. Blankenhorn points out the irony that the greatest opponents of marriage, the brigade of the Full Stacey, are the strongest proponents of same-sex marriage. The most aware anti-marriage leaders (like Judith Stacey herself) are deliberately promoting gay marriage in order to end all marriage as a social institution. They want to save the village in order to destroy it.