[I never liked the reasoning that gays have equal rights because they can marry someone of the opposite sex.]
Well, liked or not, it's legitimate.
They are not asking for "equal rights." They are demanding that we redefine marriage to accommodate their personal identity issues. Their sin, their perversion, has become the pillar of their identity... so much so that their day to day functioning depends on pretending as hard as they can that it's a "normal, healthy, and happy lifestyle." And even though they know better, they have convinced themselves that they will be happy and "normal" once they force everyone, by law, to pretend along with them.
Demanding to have the government identify and register them as "married" is nothing more than another facet of the effort to make it a crime, with tangible legal penalties, to call homosexual behavior a sin. Perhaps this hasn't registered yet, but once they get this law rammed down the throat of the legal system any organization, no matter whether private, public, secular or religious, that refuses to "recognize their union" for moral reasons or even reasons of simple sanity will be punished severely by the law.