This article addresses that question in an interesting way, by examining the difference between attitudes as one between two ideals of family: the Inherited Obligation family (living within the circle of people you were born into, and having your role be defined by your position therein) and the Negotiated Commitment family (what a lot of us call the "family of choice," the community of friends and relatives that we choose to depend on). The pertinent extract:

Same-sex marriage. The husband/father and wife/mother roles in the Inherited Obligation model are timeless, unchangeable, and necessary. Someone has to be the husband/father and someone has to be the wife/mother. Same-sex couples just can’t cover both roles, no matter how well-intentioned they may be.

But no comparable difficulty exists in the Negotiated Commitment model. A child has needs, and the parents have to negotiate a plan to meet those needs. Whether the parents are a mixed-sex couple or a same-sex couple - or even a single parent with a lot of committed friends - the problem is the same.

If the government recognizes same-sex marriages and same-sex couples as parents, then it is tacitly siding with the Negotiated Commitment model of marriage and parenthood, and undermining the Inherited Obligation model. This is why conservatives believe that marriage needs to be “defended” from same-sex relationships. But from the Negotiated Commitment point of view, “defense of marriage” is nonsense. How a same-sex couple negotiates its relationship has no effect on the negotiated relationships of mixed-sex couples.

It's a fascinating article, and well worth the read.