Largely, to: (1) simplify life for people who want to do a fairly common thing, establishing a fairly comprehensive mutual support partnership, and (2) encourage people to do that thing, and thereby reduce the chance of becoming a public burden.
> The second point of burden pertains mostly to giving tax breaks to married couples.
The "break" is mostly (roughly) treating married couples as if their combine income were earned equally split between the two, on the premise that the lower earning member of the couple is making sacrifices to enable the higher-earning member to earn their wage (for couples of roughly equal income, there is no tax break [1].)
[1] And, potentially, its worse than just "no break": http://en.wikipedia.org/wiki/Marriage_penalty
I don't want to be mean, but this logic is just faulty. You can define any discrimination as equality if you shuffle the terms around.
Think instead about marriage equality meaning equality for couples, rather than individuals. The proposal is that a same-sex couple should have the same rights as an opposite-sex couple. Discrimination is based on the collective gender of the couple.
(Update: your point about race is great and forcing me to rethink my stance by the way.)
What is the purpose of marriage benefits? How does having them benefit society enough that government wishes to recognize it? I'd guess its to encourage offspring in order to continue future prosperity. I'm proposing we step back and ask, what's the purpose of recognizing marriages? What are we trying to incentivize and is it working?
Rather than blindly extending things perhaps we should consider repealing or scaling them back? Look at the war on drugs, we thought banning marijuana would be beneficial, we're now questioning that.
The second point of burden pertains mostly to giving tax breaks to married couples.