In the article, we argue that as a moral reality, marriage is the union of a man and a woman who make a permanent and exclusive commitment to each other of the type that is naturally fulfilled by bearing and rearing children together, and renewed by acts that constitute the behavioral part of the process of reproduction.
In other words, gays should not be allowed to marry because to have a "real marriage" (those aren't scare quotes -- the authors actually use that term in the paper) you have to make kids, or at least go through the motions.
To form a real marriage, a couple needs to establish and live out the kind of union that would be completed by, and be apt for, procreation and child‐rearing.53 Since any true and honor‐ able harmony between two people has value in itself (not merely as a means), each such comprehensive union of two people—each permanent, exclusive commitment sealed by organic bodily union—certainly does as well.
Any act of organic bodily union can seal a marriage, whether or not it causes conception.
How fortunate for infertile heterosexual couples. But what about people who choose not to have children and implement that choice with artificial birth control? Should they too be barred from getting married?
Funnily enough, the paper doesn't address that question. It also doesn't address the question of whether, say, a couple that puts their child up for adoption should have their marriage annulled.
This paper appears in the Harvard Journal of Law & Public Policy an apparently respectable academic journal. I am not impressed by their standards of scholarship. (I am, however, impressed by their euphemisms. "Organic bodily union" has got to be the most highfalutin' way I've ever heard of saying "fuck.")