I will try to keep my reply short... LOL
It mainly has to do with RIGHTS. They want the RIGHT to marry legally just like other couples, plain and simple. Just like through out history... women wanted the right to vote, and work, just like MEN had, and earn large incomes like men, so THEY fought for it. African Americans wanted the RIGHT to be free, get paid for labor, vote and etc... just like WHITE people had the RIGHT to, so they fought for it. I could go on here, but I hope you get the idea. Through out history, people, or a type of people have fought for the same RIGHT or RIGHTS given to other types of people. We are supposed to be "all created equal" but we are not.
I know Christians will stand by "if is a sin in GOD's eyes, and they should not be allowed to be married and etc..." BUT if you know your history, or if not then look it up... but back in the day, during slavery and before, Christians and others said the EXACT same thing about African Americans. They used to preach that African Americans were NOT GOD's children, and etc... so they too were not allowed to get married for it would be considered a "sin" and etc... It used to be a SIN for women to work, or do anything other than stay home, cook, clean, get pregnant, and take care of the husband. According to the bible, a woman could be stoned to death for not obeying her husband, or for not giving him a child. Yes this is old testament, but it is STILL what was true back then, and what we humans believed, and what the bible said GOD felt or etc...
As with most things, things change, times change and etc... so NOW well now as in since back then, LOL, all of a sudden it is NOT a sin for African Americans to marry, it is NOT a sin for a woman to work, it is not a SIN for a woman to have a life separate from her husband, and to vote and etc... YET it is STILL a sin for the same sex to get married? I am sorry but it is just to damn convenient, to me. I feel it is just to much based on what the current society feels and thinks about the matter or issue at the time. More importantly it is just what MAN thinks, or feels is a SIN, RIGHT or ACCEPTABLE at the time that influences things more than anything.
Another thing to sort of prove my point here... homosexuality is simply that, regardless if it is two men, or two women, it is still "homosexuality"... BUT in today's times, and for a LONG time, actually though out history too, 2 women together has been more accepted than 2 men. THIS IS BS. If you want to bash homosexuality, then bash BOTH types, not just men/men. Do not tell me "oh it is a sin and wrong for two men to be together" yet turn around and have a threesome with your wife/girlfriend and another woman, or watch a *bleep* and *bleep* to two women, or fantasize about them and etc... THAT is just plain prejudice, and it is bias.