No, actually marriage is a universal, natural human institution, and in that sense is secular, in that it pre-exists all extant human religions (unless you want to posit that some animist religion in Africa practiced by some tiny tribe might pre-exist marriage), exists in all societies past or present, regardless of their religious commitments, from the India of the Vedas to modern India, from animist ancient Korea to atheist North Korea and mixed Christian/Buddhist South Korea, from the pagan society of Ur which Abraham left to the modern Near East with its mix of Jews, Muslims and Christians, from the homogeneously Orthodox Christian Republic of Novgorod to its contemporary, the religiously pluralist Mongol Empire, from the Puritan Massachusetts Bay Colony to the modern United States of America.
In some societies it has been closely regulated by the state, in others the state simply recognized it as a fact. In some polygamy is or was permitted or marriage coexisted with some sort of legally regularized concubinage. In some marriages were or are grounded in what we now call romantic love, in others, they were or are arranged by the families of the spouses-to-be. But the basic nature of the institution is the same, and the notion that the parties need not be a man and a woman is an absurdity.
Its origins are biological, as Our Lord Jesus Christ commented on it during His earthly ministry when he criticized the Mosaic permission for divorce, and to the secular-minded it can be defended and explained on purely Darwinian grounds as optimizing the survival chances of offspring (or even of “selfish genes”): since human children require nurture, creating a stable, socially supported bond between a male and a female likely to have offspring ensures that children are more likely to be raised by those with whom they share the most genetic material — their biological parents. This fact also accounts for the traditional tendency to favor grandparents, adult siblings, or failing that aunts and uncles as adoptive parents for orphans.
That is a remarkably thorough explication of the nature of marriage as the relationship of a man and a woman. Alternatives are historically, morally, biologically, religiously, socially and politically ridiculous. We live in the age of ridiculous.