Harvard's Robert George (et. al.) writes: "What we have come to call the gay marriage debate is not directly about homosexuality, but about marriage. It is not about whom to let marry, but about what marriage is. It is a pivotal stage in a decades-long struggle between two views of the meaning of marriage." (Girgis, Sherif; Anderson, Ryan T; George, Robert P; What Is Marriage?: Man and Woman: A Defense, Kindle Locations 72-74)
The two views are:
1) The conjugal view of marriage. This "is a vision of marriage as a bodily as well as an emotional and spiritual bond, distinguished thus by its comprehensiveness, which is, like all love, effusive: flowing out into the wide sharing of family life and ahead to lifelong fidelity. In marriage, so understood, the world rests its hope and finds ultimate renewal." (Ib.)
2) The revisionist view of marriage. This "is a vision of marriage as, in essence, a loving emotional bond, one distinguished by its intensity—a bond that needn’t point beyond the partners, in which fidelity is ultimately subject to one’s own desires. In marriage, so understood, partners seek emotional fulfillment, and remain as long as they find it." (Ib., Kindle Locations 78-80)
Re. 1, "comprehensive union is valuable in itself, but its link to children’s welfare makes marriage a public good that the state should recognize and support." (Ib., Kindle Locations 106-107)
"There is nothing specifically homosexual about the revisionist view of marriage. It informs many male-female relationships. But it brooks no real difference between these and same-sex relationships: both involve intense emotional union, so both can make a marriage. Comprehensive union, by contrast, is something only a man and woman can form." (Ob., Kindle Locations 113-116)
Therefore, to enact same-sex would not expand the institution on marriage. It would redefine it.