Well, lets start this off simply.
1. What is a "marriage"?
Dictionary: mar·riage (măr'ĭj) pronunciation
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1. The legal union of a man and woman as husband and wife.
2. The state of being married; wedlock.
3. A common-law marriage.
4. A union between two persons having the customary but usually not the legal force of marriage: a same-sex marriage.
2. A wedding.
3. A close union: “the most successful marriage of beauty and blood in mainstream comics” (Lloyd Rose).
4. Games. The combination of the king and queen of the same suit, as in pinochle.
2. What types of marriages exist in various societies?
Typically people talk of just 3 types of marriages:
Polygamy, monogamy, and polyandry
These 3 types of marriage are defined as, 1 man - many women, 1 man - 1 woman, 1 woman - many men.
3. Other types of marriage:
Getting married to a plant:
Some parts of India follow a custom in which the groom is required to marry with an auspicious plant called Tulsi before a second marriage to overcome inauspicious predictions about the health of the husband. This also applies if the prospective wife is considered to be 'bad luck' or a 'bad omen' astrologically. However, the relationship is not consummated and does not affect their ability to remarry later. One should note that this is not a norm found across the entire Indian sub-continent.
# Ghost marriage -(among the Nuer of Southern Sudan)- a woman marries a man from the tribe that died before he could marry.
# Group marriage - A form of polygamous marriage in which more than one man and more than one woman form a family unit, and all members of the marriage share parental responsibility for any children arising from the marriage
same-sex marriage - Marriage between two people who are of the same sex.
open marriage - A marriage in which the partners agree that each is free to engage in extramarital sexual relationships, without regarding this as sexual infidelity.
Human-animal marriage - A marriage between a human and a non-human animal. http://en.wikipedia.org/wiki/Human-animal_marriage
My argument has basically two key components.
A. The first definition of marriage is between a Husband and a Wife. These terms are meaningless with a same sex marriage. This shows us, that the concept of marriage, and Husbands and Wives, is defined by the joining of opposite sexes. Even while different cultures have different details of what exactly a "marriage" is, in common understanding of the term, all of been defined as the joining of opposite sexes.
B. In cases where the joining of the opposite sexes are not recognized, these types of marriages have been put aside as either deviant, immoral (by some), or symbolic in nature only.
If one wishes for the law to recognize some extra-cultural marriages, then one must be willing and advocating for the recognition of ALL marriages. By extra-cultural, I refer specifically to marriages that the country in question has not historically recognized as being valid.
It would be illogical and immoral to open up the legal definition of marriage to include some but not all variants.
edit: p.s. I labeled my arguments with numbers and letters, so you can just refer to those instead of quoting entire posts.