You can define 'marriage' however you want. Nobody cares.
What people care about is treating some people differently in the eyes of the law. Either remove the economic advantages given to married couples or grant those benefits to ALL married couples.
This is NOT rocket science!
Apparently it is rocket science. If all men and all women are treated the same, that's called equality. Any eligible man can marry any eligible woman. Changing it to include men with men and women with women is a special consideration and has zip to do with equality. You can't be more equal if it's already equal.
The exact same logic was used when interracial marriage was banned. Blacks and white were both subject to the law, so it was 'equal'. Allowing them to marry each other was a 'special consideration' and had 'zip to do with equality'.
It was a bullshit argument then. And nearly 50 years later, its still a fetid corpse of an argument. As the standard itself is invalid, unjust, and unequal, with the restrictions having nothing to do with the requirements of the union.
Its the same with gay marriage. There's no requirement of marriage that gays and lesbians can't satisfy. There's no state interest in denying gays and lesbians the right to marry. And it has no rational reason. If you're going to deny someone their rights, you need a very good reason.
And opponents of same sex marriage simply don't have it.