Both, actually. You're getting out of a contract.
I mean, if you don't want to drive anymore, do you have to go to court to "nullify your drivers license"? Of course not.
But you do have to take legal action to get out of a legal contract - like a marriage.
Okay look, if it was just a "verbal contract" between the two individuals, then same sex marriage would be recognized by the states and no marriage license would be required, nor signatures, etc. We wouldn't have to vote and go to courts to make the contract between same sex couples legal. Obviously, the contract is not a verbal one between "two people and their [supposed] god" (if they have one). At least, not legally recognized marriage. No one is arguing that people can go off and get married to whomever or whatever they wish using whatever ceremony they deem fit. But in order for it to be legally recognized, there must be a govt recognized, legal contract between the individuals in question. Otherwise, it's not a govt recognized marriage offering the privileges and obligations to the people who agreed to enter into said contract.
I completely support removing the government from the process and keeping marriage a purely social and private institution. Absolutely, 100% agree. However, currently, it is a legal contract that discriminates based on gender. And as long as it is a legal contract, then it cannot be allowed to discriminate based on gender.