Omega:
First of all, where is this "Natural Law" you keep citing? Where can I find a copy?
Now, the post from the earlier thread is far more relevant than you think, but I'll outline the points more clearly:
Let's say there is a Natural Law which wants one man and one woman to be monogamous. Even if there is one, it doesn't matter. We're not discussing what is natural according to some book or ancient worldview. We're talking about what is legal.
Legally, men and women can be married but don't necessarily have to act in the traditional, Christian, monogamous way. A man and woman can get married and have sex on the side. A man and woman can get married and have sex on the side with people of the same gender. A man and woman can get married but refuse to have sex whatsoever and only have sex with other people (some of which, what the hell, can be of the same gender). A man can get married to a woman, but never talk to her, and instead room with and have sex with one other man, monogamously, for the rest of his life. A man and woman can get married and, god forbid, practice anal sex. Christianity is unhappy with all of these married couples, and I'm sure they're failing to go along with your "Natural Law" in some way.
Married people have these rights because the government A) it doesn't have the power to police the personal lives of its citizens in this way and B) the government doesn't have anything to do with the Church anyway, which is the only organization that might care what people are doing in the bedroom. So what, legally, is marriage? It's basically just a piece of paper that gives you (and a partner to whom you consent to be legally tied) a number of legal privileges. Marriage as it exists today doesn't have anything to do with any Natural Law whatsoever.
So we've got a legal institution that ties men to women, but this tie isn't morally or spiritually significant in any way. Great. So why should same-sex marriage be legal? Let's take a step back:
Mark is a capable male adult.
Jerry is a capable male adult.
Craig is a capable male adult.
Cara is a capable female adult.
Synthia is a drawing of a capable female adult.
Cara and Craig can marry. This is because they are capable adults.
Mark and Jerry are both capable adults, but the state doesn't recognize their marriage. This isn't really fair, given that the marriage of Craig and Cara affords them several perks that Mark and Jerry won't get, even if they commit to one another informally. Because they're capable adults, you would assume that Mark and Jerry would be able to marry if you saw them on the street individually, but this isn't the case for some reason. This disparity, according to supporters of the gay rights movement, should be rectified.
Mark and Synthia cannot marry. Mark is a capable adult but Synthia is a drawing and cannot give consent. Only the very confused would argue for Mark and Synthia's marriage. Mark and Jerry's marriage makes sense because they are both adults and should be able to consent to marriage, but Mark and Synthia's doesn't, even though Mark is male and Synthia is (a drawing of a) female.
Basically, you don't have to think gayness is legitimate. I don't care if you think all gay people are violating "Natural Laws". But the government's failing to recognize gay marriage is nothing short of unfair, and legalizing gay marriage is the only way to achieve equality.
(A few spare notes: homosexuality does occur in nature. Monogamy is quite uncommon in nature. The definition of marriage as being "between a man and a woman" is very recent indeed - the Defense of Marriage Act was signed into law in '96 (thanks Wikipedia). A few governments are still rushing to define marriage as being between a man and a woman (see beginning of this thread) -- the "definition of marriage" argument doesn't really work in that respect.)