Along the way, she makes what one might call a secular liberal argument for sanctity, and for recognition by the secular state of what one might call sacred events.
She doesn't call it that at all, but she effectively argues that certain life experiences, such as birth and death, are so inherently invested with transcendent significance that any society, no matter how secular or rationalist, must accord them special treatment. Sounds like sanctity to me.
Some excerpts (emphasis mine):
Update (Aug. 19): I've trimmed these excerpts further, since they were too long for easy reading.
Families are not infinitely malleable, as even champions of diversity must concede. This does not simply owe to considerations of size: A government that distributed children randomly, for example, could not be other than tyrannical. Even if it had the best interests of society in mind -- say, the principle of equal opportunity, radically understood -- a government that paid no regard to the claims of biological parenthood would be unacceptable to all but the most fanatical of egalitarian or communitarian zealots. Beyond its other functions--limiting female fertility, transmitting property, or providing companionship, for example--marriage is a way of honoring this central fact, which limits one's ability to regard practices of marriage as either wholly dependent on belief in a particular divine revelation or as wholly "socially constructed."
But marriage is not merely a matter of biology. That children can be "illegitimate" suggests that the biological facts of parenthood are not enough for social purposes. Disputes over fatherhood, for example, or variations in parental attachment to their children, make it reasonable for societies to supplement and sometimes override the natural bonds established by and through the processes of human generation. Marriage is, before all else, the practice by which human societies mark, modify, and occasionally mask these bonds. Like death, and the funereal rites that universally accompany it in one form or another, human generation has a significance that is more than arbitrary, if less than obvious. Marriage is the primary way societies interpret that significance, and it is doubtful whether any other custom could substitute for it adequately.
Generation and death
When considering the institution of marriage, a useful comparison exists between how society addresses the beginning and end of human life. Like death, our relation to which is shaped and challenged but not effaced by modern technologies, generation defines our human nature, both in obvious ways and in ways difficult to fathom fully. As long as this is so, there is a special place for marriage understood as it has always been understood. That is to say, there is a need for society to recognize that human generation and its claims are an irreducible feature of the human experience.
Like the rites and practices surrounding death, marriage invests a powerful, universally shared experience with the norms and purposes of a given society....
... If it is discriminatory to deny gay couples the right to "marry," is it not equally unfair to deny living individuals the right to attend their own "funerals"? If it makes individuals happy, some would reply, what is the harm? Only that a society without the means of formally acknowledging, through marriage, the fact of generation, like one without the means of formally acknowledging, through funeral rites, the fact of death, seems impoverished in the most basic of human terms.
Like generation, death has a "public face" so obvious that we hardly think of it. The state issues death certificates and otherwise defines death legally. It recognizes funeral attendance as a legal excuse in certain contexts, such as jury duty. It also regulates the treatment of corpses, which may not merely be disposed of like any ordinary animal waste. Many states afford funeral corteges special privileges not enjoyed by ordinary motorists. Funeral parlors are strictly regulated, and there are limits on the purchase and destruction of cemeteries that do not apply to ordinary real estate. In short, there are a number of ways in which a liberal democratic government, as a matter of course, both acknowledges "death" and limits the funereal rites and practices of particular sects and individuals. I cannot call a party in my honor my "funeral" and expect the same public respect and deference afforded genuine rites for the dead. And it would be a grim society indeed that allowed people to treat the dead any old which way -- as human lampshades, for example.
It's worth reading the whole essay while you're at it.