Let's take some time to summarize the arguments that have been made:
1. Marriage is exclusively for the purpose of procreation.
counter argument: There are other reasons to enter into a marriage.
For the counter, I've listed other reasons, and have given examples of heterosexual unions that are entered into for purposes other than procreation.
Niminus counters with this quote:
(1) Men and women of full age, without any limitation due to race, nationality or religion, have the right to marry and to found a family. They are entitled to equal rights as to marriage, during marriage and at its dissolution.
Where does it say "heterosexual men and women?
(2) Marriage shall be entered into only with the free and full consent of the intending spouses.
That should be a given, even if some cultures do have arranged marriages.
(3) The family is the natural and fundamental group unit of society and is entitled to protection by society and the State.
Yes, that's so. It doesn't support the counter argument, but it is true.
Article 25.
(1) Everyone has the right to a standard of living adequate for the health and well-being of himself and of his family, including food, clothing, housing and medical care and necessary social services, and the right to security in the event of unemployment, sickness, disability, widowhood, old age or other lack of livelihood in circumstances beyond his control.
That one would make a good argument for another thread, perhaps one on universal health care. It doesn't say that procreation is the only reason for a marriage.
(2) Motherhood and childhood are entitled to special care and assistance. All children, whether born in or out of wedlock, shall enjoy the same social protection.
Yes, all children should have protection, special care, assistance. Children are our future, are our most important citizens. Where does it say that children are the only reason for marriage?
Argument 2: Children can't be conceived by a homosexual couple.
No, that simply is not biologically true. Any woman who is fertile can conceive a child. Anyway, argument 2 depends on argument 1, that the sole purpose for marriage is procreation. That argument has not been supported.
Not only that, but there are heterosexual marriages that are not formed to produce children: Marriages between seniors, marriages between people who don't want children, and marriages of women who are infertile for example. If you're going to argue that gay marriage should not be allowed because the couple in question can't have a biological child of their own, then the argument must extend to heterosexual marriages in which childbirth is not the purpose.
The logical arguments against allowing gay marriages are not tenable. The only real arguments are based on emotion and religious conviction.