I was thinking about this issue a few days ago and I recalled two things that occurred in my life in 1972 (when dinosaurs roamed the earth) that had to do with my so-called rights.
In 1972 I was 19 (I turned 20 in September). I was a voting-age citizen of the United States and the bearer of all rights therein. In the Spring of that year I received a letter that began with the word, "Greetings!" It was my draft notice. I learned very quickly that my right to do what I wanted had been suspended. I did not have the right to refuse that summons to serve in the military (as it turned out, I joined the Navy and served four years). Yes, the summons to compulsory military service came with the privilege of being a citizen, but my rights to individual freedom had to be suspended for that to happen.
The second thing that happened that year is that I got engaged. Emily and I made a verbal commitment to each other and it was affirmed by our community and families. We had the "right" to just move in together (which we did not), but getting married turned out to be different. In 1972, three things had to happen for us in order to get married: (1) We had to get blood tests. Presumably we would have been refused a marriage license if something suspect was shown in the test results; (2) I had to get my parent's written permission. In 1972, a woman could marry at 18, but a man had to be 21 (probably a wise recognition of the disparity between maturity levels). I could get married at 20, but my parents had to give me a letter (which they did); (3) A recognized official (clergy, officer of the court, etc.) had to preside over a marriage ceremony, religious or otherwise.
For us, marriage was not really a right--it was a request we made to the state of California that could be denied under certain circumstances. People, for example, who are already married cannot get married to another person--the permission will not be granted.
In 1972, two people of the same sex could not receive permission to marry. But since that time, other restrictions to the permission process have been lifted: Blood tests are no longer required; people may marry at age 18 (both male and female). Some sort of ceremony by an authorized person is still required, however. It is still a granting of permission and the conferring of legal recognition.
When people get married, I don't think they are exercising a right. It is the receiving of recognition by the larger community (in our case, the state of California) that this relationship qualifies for the protections offered by the legalities of marriage, including ownership of property, rights to income, inheritance, structures for offspring, etc. In an important way, marriage has always been an institution that protects the couple, but also serves the community.
I think the argument about rights in same-sex marriage is misplaced. Perhaps the proponents should talk about how (1) they believe same-sex as a limiter should be simply removed from the list, just as blood tests and parental permission have been; (2) they believe that same-sex marriage, in a recognition by the state, serves the larger community.
Christians should look at the issue a little differently, I believe. For us, marriage is also not about rights. Marriage is about a covenant relationship that is characterized by faithfulness--to God, to each other, and to our community. Marriage is not simply a contract that is characterized by rights. We also believe that marriage is a spiritual and theological reality--it is a reflection of the image of God (we get this from Genesis chapters 1-2 in the Bible). More on this topic later.
If marriage is only about rights, then there can be a lot of movement to remove more and more limiters from those rights: Change the legal age of adulthood from 18 to 10. That would allow a 40-year-old man to marry an 11-year-old girl--it would be his right to do so. Change the requirement that marriage be monogamous--people could have the right to marry as many people as desired. If marriage is only about rights, then that right should be exercised as anyone sees fit. If not, then there must be discrimination afoot.
The argument regarding the rights of marriage is painful because it is misplaced. If there is an argument, at least from the legal side, then it needs to framed differently.