There is a wonderful essay answering that question in the Harvard Journal of Law and Public Policy. The authors are Sherif Girgis and Robert George of Princeton and Ryan T. Anderson of Notre Dame. You can download it here. We've excerpted a portion below.
B) Real Marriage IS--And Is Only--The Union of Husband and Wife
As many people acknowledge, marriage involves: first, a comprehensive union of spouses; second, a special link to children; and third, norms of permanence, monogamy, and exclusivity. All three elements point to the conjugal understanding of marriage.
1) Comprehensive Union
Marriage is distinguished from every other form of friendship inasmuch as it is comprehensive. It involves a sharing of lives and resources, and a union of minds and wills—hence, among other things, the requirement of consent for forming a marriage. But on the conjugal view, it also includes organic bodily union. This is because the body is a real part of the person, not just his costume, vehicle, or property. Human beings are not properly understood as nonbodily persons—minds, ghosts, consciousnesses—that inhabit and use nonpersonal bodies. After all, if someone ruins your car, he vandalizes your property, but if he amputates your leg, he injures you. Because the body is an inherent part of the human person, there is a difference in kind between vandalism and violation; between destruction of property and mutilation of bodies.
Likewise, because our bodies are truly aspects of us as persons, any union of two people that did not involve organic bodily union would not be comprehensive—it would leave out
an important part of each person’s being. Because persons are body‐mind composites, a bodily union extends the relationship of two friends along an entirely new dimension of their being
as persons. If two people want to unite in the comprehensive way proper to marriage, they must (among other things) unite organically—that is, in the bodily dimension of their being.
This necessity of bodily union can be seen most clearly by imagining the alternatives. Suppose that Michael and Michelle build their relationship not on sexual exclusivity, but on tennis
exclusivity. They pledge to play tennis with each other, and only with each other, until death do them part. Are they thereby married? No. Substitute for tennis any nonsexual activity
at all, and they still aren’t married: Sexual exclusivity— exclusivity with respect to a specific kind of bodily union—is required. But what is it about sexual intercourse that makes it
uniquely capable of creating bodily union? People’s bodies can touch and interact in all sorts of ways, so why does only sexual union make bodies in any significant sense “one flesh”?
Our organs—our heart and stomach, for example—are parts of one body because they are coordinated, along with other parts, for a common biological purpose of the whole: our biological life. It follows that for two individuals to unite organically, and thus bodily, their bodies must be coordinated for some biological purpose of the whole.
That sort of union is impossible in relation to functions such as digestion and circulation, for which the human individual is by nature sufficient. But individual adults are naturally incomplete with respect to one biological function: sexual reproduction. In coitus, but not in other forms of sexual contact, a man and a woman’s bodies coordinate by way of their sexual organs for the common biological purpose of reproduction. They perform the first step of the complex reproductive process. Thus, their bodies become, in a strong sense, one—they are biologically united, and do not merely rub together—in coitus (and only in coitus), similarly to the way in which one’s heart, lungs, and other organs form a unity: by coordinating for the biological good of the whole. In this case, the whole is made up of the man and woman as a couple, and the biological good of that whole is their reproduction.
Here is another way of looking at it. Union on any plane— bodily, mental, or whatever—involves mutual coordination on that plane, toward a good on that plane. When Einstein and Bohr discussed a physics problem, they coordinated intellectually for an intellectual good, truth. And the intellectual union they enjoyed was real, whether or not its ultimate target (in this case, a theoretical solution) was reached—assuming, as we safely can, that both Einstein and Bohr were honestly seeking truth and not merely pretending while engaging in deception or other acts which would make their apparent intellectual union only an illusion.
By extension, bodily union involves mutual coordination toward a bodily good—which is realized only through coitus. And this union occurs even when conception, the bodily good toward which sexual intercourse as a biological function is oriented, does not occur. In other words, organic bodily unity is achieved when a man and woman coordinate to perform an act of the kind that causes conception. This act is traditionally called the act of generation or the generative act;if (and only if) it is a free and loving expression of the spouses’ permanent and exclusive commitment, then it is also a marital act.
Because interpersonal unions are valuable in themselves, and not merely as means to other ends, a husband and wife’s loving bodily union in coitus and the special kind of relationship to
which it is integral are valuable whether or not conception results and even when conception is not sought. But two men or two women cannot achieve organic bodily union since there is no bodily good or function toward which their bodies can coordinate, reproduction being the only candidate. This is a clear sense in which their union cannot be marital, if marital means comprehensive and comprehensive means, among other things, bodily.