How should we approach this issue? First, we need to understand what the Bible says about marriage. Second, we need to understand that our secularizing world will not care what the Bible says, and so the arguments we make for heterosexual monogamy ought to be primarily apologetic in nature.
From the first, we must admit that the evangelical church has done a lousy job on marriage in its own ranks. Well might the homosexual activist say that evangelicals believe that marriage is between a man, and a woman, and a woman, and a woman.... It is wrong to argue that homosexual marriage will kill the institution of marriage. The sexual revolution and the rampant divorce that followed in its wake have all but killed the stabilizing institution of marriage. We need to give kudos to the Roman Catholic Church on this point --they have not yielded to popular pressure or practice. Yes, there is some hypocrisy --granting annulments and so on, but their stance remains: the Catholic church is firmly against divorce.
Some Christians have wrongly sought to abandon any public or legal protections for the institution of marriage. If marriage were not a government issue, then we would not be having this discussion. This is true, but hardly consistent with a Christian world-and-life-view, which is why I say that we must come to understand marriage Biblically.
Rome is wrong here: marriage is not a sacrament. Sacraments are means of grace for believers and marriage is for all men and women. It is not a private religious contract between a man and a woman, but something undertaken for both private benefit and public good. It is good for children to be raised in two-parent homes. It stabilizes society and prevents poverty and every study ever done bears that out. That is an apologetic argument for why government should recognize and sanction marriages, though it does not answer the question of why two men or two women ought or oughtn't to be able to marry.
Theologically, we understand that marriage is a common-grace ordinance. It is written into creation itself, and not just for Christians. A pluralistic society can never grasp this teaching, since it believes that the Bible is simply one religious book among many. Some point out that the current institution of marriage (one woman and one man, for life) is of relatively recent vintage and that Scripture itself contains abundant examples of believers who did not follow this example. Genesis, however, is an ancient document (roughly 3500 years old) and Jesus draws his teaching from the very beginning of Genesis. God's original intent and design was not polygamy, though believers did certainly engage in it. Yet, without exception, polygamy introduced grief into the households where it was practiced (the deadly rivalries between Isaac and Ishmael, Joseph and his brothers, and among the children of King David). It did so because it departed from God's design.
Although somewhat tangential to the main case, apologetically we might argue that polygamy creates nothing but problems: rivalries among wives and among the children of different wives, and a shortage of marriageable women (since the birthrate of males and females is roughly the same, polygamy inevitably creates too few marriageable females). Those who would argue that the federal government's interest in "traditional marriage" is relatively recent might consider that the Federal Government denied Utah statehood from at least the 1850's in large part due to the LDS practice of polygamy. The government has long realized that it has a vested interest in promoting stable monogamous heterosexual marriages.
What we must draw from this is:
1.) God has a particular design for marriage.
2.) Departures from that design bring misery (as in the case of polygamy and divorced and unwed motherhood).
Yet, living in a pluralist society, how can we make a commonsense apologetic case for the protection of monogamous heterosexual marriage in law? I think too often our arguments are weak. For instance, the "marriage is chiefly for procreation" argument is deeply flawed. Theologically, we understand that marriage is not chiefly for procreation but companionship. You do not have to be capable of procreation to marry. Infertile people can marry; people past childbearing years can marry. Likewise, the definition argument fails --it is mere semantics to argue "Well, the definition of marriage is a union between a man and a woman, therefore marriage can only be between a man and a woman." It's a sad day when we have to resort to a dictionary to make our arguments, and definitions change over time. We don't have an unchanging language authority.
We must understand, too, that we are losing this battle, and are probably going to lose it definitively and for good in the very near future. It shouldn't be a cause for rejoicing that 60% of North Carolinians who voted did so in favor of protecting heterosexual marriage. Our focus should be on the 40% who didn't. 40 years ago, that would have been unthinkable. 20 years ago, the number may have been 90/10.
That said, it is important we make the case. We need to make it to our own children. The younger generations of evangelicals are softening towards homosexual practice and we need to teach carefully how we in the church are to regard homosexuals and their desire to marry. Too often, our stance has been motivated by somewhat of an "ick" factor (conservative Christians who were unruffled when pastors in their denominations were exonerated while preaching that Jesus did not rise from the dead are leaving their denominations in droves for ordaining and marrying homosexual persons, which I find troubling). Mark Yarhouse's book Homosexuality and the Christian is a good place to start.
Why is it, from an apologetic standpoint, that state recognition of homosexual marriage is a bad idea? Theologically we understand --God created man and women to be together in a one-flesh, companionship, head-helper relationship. We know that any deviation from the norm brings misery. Therefore, we ought to want to prevent people from experiencing misery.
How do we, then, make the argument? I think presuppositionalism helps us here --in other words, the best way to win an argument is to look for the weaknesses or inconsistencies in your opponent's argument. You don't have to be harsh or unloving as you do this, but gently pointing out inconsistencies in his case will build the case for the truth. Presuppositionalism is built on the premise that the truth is a coherent whole and any false system will have cracks and flaws --find those and you can advance the truth.
I think the case might advance this way. What is marriage, after all, and where does it come from? Is it mere social convention, or something more? What does it mean? Why is it significant? Is it only an emotive response --somehow solemnizing the fact that humans have some desire to mate for extended periods of time, not unlike geese or cardinals? Why is it a desirable state to be sought by anyone, let alone homosexual persons? Nothing hinders homosexual men or women from living together, committing to one another for life, from engaging in sex, or solemnizing such with a ritual. Why is it that civil marriage is a desirable state? Is it for tax purposes? Is it for the right to make end-of-life sorts of decisions for a much-beloved companion?
In short, it is generally true that the burden of proof falls upon the one introducing the novelty. What argues in favor of the change? If modern Western society has upheld heterosexual monogamy as the ideal for two millennia (and arguably much longer), and, moreover, this practice also prevails in the Orient, why is it so? Is it merely an evolutionary response --that it's better for offspring to pair for extended periods?
I would hazard a guess that most homosexuals would argue that marriage is of far more significance than the benefits listed above. Here is where the point could be pressed --but why is it more, what invests it with such significance? How can it really "mean" anything apart from its religious moorings? And how could it mean anything if those religious moorings are just made up? What is it in us that makes us desire a relationship that causes so much pain, is so unstable, calls for so much self-sacrifice, and so often fails?
I am just putting this out there. I don't know how strong it is, really, but I have yet to see it tried. We must realize, however, that rationality doesn't always win the day. One could make a rational and logical case, but if another person is heavily personally invested in his lifestyle, rationality won't change his mind. The Holy Spirit, however, just might.