You keep saying this... but what would it solve, really? Homosexuality's defining characteristic is a certain behavior. Whether it's something innate or acquired, what changes?
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1) Of course it is- that's what laws do. We discriminate against people who speed. We descriminate against people in certain income brackets, ect. Almost all law is about treating people who meet certain conditions differently. Certain basic rights are supposed to be beyond the reach of government, but even these are not without limit.
2) Here I would say no.
3) Does being single confer a second-class status? Does being married confer a first-class status? On all of these, I would say no.
4)N/A. See #3.
5) You're asking the wrong question. I think you should ask instead 'What is the state's purpose in granting special recognition to married couples?'. The state shouldn't be in the business of granting bennies to people because they're in love- that's pointless. Streamlining legal processes to make for a stable environment to rear children, simplify inheritance, ect could be valid reasons.
My conclusion: Considering government recognition of marriage as a fundamental right is a flawed premise. People are free to fall in love with whoever they want, have sex and children with whoever they want- government recognition neither allows or prevents that. This is where the debate so often goes wrong. We're talking about extending government recognition and certain benefits to couples that match set criteria. People can make the argument that it's to the benefit of society for same-sex couples for get such recognition and if they can convince enough people, they'll get it. Personally, I don't see the need for it, and am therefore not agitating for same-sex marriage. However, if it comes to pass it's not going to be the end of the world either. I do admit that I get a little annoyed in the aggressive manner that proponents choose to shove it down our throats.

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