I'm not sure this is true. In ~350 Emperor Constantius II ordered executions of people who were same-sex married, and outlawing it going forward. It seems this law would be unnecessary if legal, same-sex marriages weren't rarely occurring and legally recognized in Republican Rome. Also, Nero famously married two men, so there were at least two legally recognized Roman same-sex marriages, if only legal by will of the emperor.
Also, many traditional societies (the Gikuyu and Nandi for instance) have same-sex or third-sex marriage as a legal practice to deal with inheritance. Its purpose is not sexual, but nothing stops it from becoming so. Native American tribes had marriages between berdaches and men. The fuijan, in China, also had religious same-sex marriages (I have no idea if they were legally, but according to Passions of the Cut Sleeve they were socially recognized).
Emperor Nero was known for being a weirdo, hence I wouldn't consider him as representative of Roman culture.
Anyway, according to Wikipedia, stable or semi-stable same-sex relationships were given some degree of legal recognition in Rome and other ancient societies, hence it appears that my original claim should be weakened.
Suppose I told you that I knew for a fact that the following statements were true:
You’d think I was crazy, right?
Now suppose it were the year 1901, and you had to choose between believing those statements I have just offered, and believing statements like the following:
Based on a comment of Robin Hanson’s: “I wonder if one could describe in enough detail a fictional story of an alternative reality, a reality that our ancestors could not distinguish from the truth, in order to make it very clear how surprising the truth turned out to be.”1
1Source: http://lesswrong.com/lw/j0/making_history_available/ewg.