Another argument for justifying the expansion of marriage to same-sex couples addressed by ‘Discussing Marriage‘ regards supposed research showing that there is no difference in the well-being of children raised by a same-sex couple than that of children raised in other family arrangements. The argument would go something like this:
P1: Research shows no difference in the well-being of children raised by a same-sex couple and children raised in other family arrangements.
P2: Children will not be harmed by being raised by a same-sex couple
C1: Same-sex marriage should be legalized
The web site linked above calls this argument something of a red-herring. The well-being of children is not a primary argument that is used to oppose same-sex marriage. The response also includes that the bulk of historical research has shown that children are better off being raised by their own biological parents than in any other arrangement. The authors of the site are critical of some recent research because of small sample sizes, lack of random sampling, cultural bias and other factors.
For more details and references I would refer you to the Discussing Marriage website.