That is true but misses the crucial point and that is the equal application of law. By blessing hetero marriages with certain advantages and then not giving that same blessing to other marriages is not an equal application of the law. It is selectively applying law to a preferred group while excluding the non-preferred group. While your above argument works well in defending the position that government should be out of marriage entirely, it fails in limiting gay marriages while still recognizing hetero ones. Laws should never apply to one group or type of people without applying evenly to other people.You would be correct if you were referring to government preventing gays from being gay. The discussion is about what government recognizes as marriage. It does not limit your life, limit or pursuit of happiness for government to not recognize your union as marriage. No one has the right to demand things of others, including government. You have the right to be left alone from government without due process. Government not recognizing gay marriage as marriage has nothing to do with preventing people from living their own lives as they see fit. Ditto interracial marriage.
That's not what equal protection means. Equal protection is when the same law is applied to different people differently. Equal protection isn't a formula, it's the same law applied the same way. You're black, you can't use this government bathroom. Clear violation. However, with gays, the law is applied the same way. Straights and gays can enter into a man/woman marriage, neither can enter into a heterosexual marriage. There is no, but I WANT something different in the law, sorry.
There is a solution, it's called the, wait for it, legislature. Do it the right way, not with word parsing formulas.
Heterosexual people can marry other heterosexual people.
Gay people CAN NOT marry other gay people.
That is not equal protection under the law no matter how hard you try to polish that turd.