On being a rationalisation rather than an argument

If the purpose of state regulation of marriage is procreation, then that is not an argument for only recognising monogamous marriage. Consider the following claim:

The state has a legitimate interest in its own perpetuation  and maintenance via the production of children, their socializing, their protection, and their transformation into productive citizens who will contribute to the common good. … It is this interest that justifies the state's recognition  and regulation of marriage as a union of exactly one man and exactly one woman. 

If procreation is the reason for state involvement in marriage, then polygamous marriage (whether polygyny or polyandry) is a perfectly reasonable way to raise children conceived within the marriage. It spreads the duty of parenting among more than two people.

Arguments for monogamy and against polygamy rest on other considerations -- such as the status of women and spreading the opportunity to be married more widely. (For example, polygyny tends to cut lower status males out of marriage opportunities.) But they do not rest on issue of procreation. This is simple rationalisation -- I have a conclusion I want (marriage as a union of exactly one man and exactly one woman) and so claim my premises support it, when they do not. 

In fact, remarkably little of the regulation of marriage rests on procreation. The state does not check on the procreative capacity of potential marriage partners, it does not require them to state any intent to procreate and it permits adoption -- the raising of children procreated elsewhere. The matter of adoption shows up how the term procreation is being used in such arguments to obscure the difference between a biological act and a social responsibility.

The raising of children is part of why marriage is regulated, but that does not require those raising the children be their procreators. Once adoption is permitted, then the "not procreative" argument against same-sex marriage falls over. Especially given the lack of any significant evidence that whether couples are same-sex or opposite-sex has any systematic negative effect on the children so raised. Moreover, the notion that the quality of the parenting can be reliably divided in such a way flies against our experience of the diversity of people as individuals and the diversity of the quality of their relationships.

Marriage is a socially preferred means of raising children, but that is due to the characteristics of marriage, it does not determine said characteristics. In particular, it does not determine that marriage be monogamous and not polygamous.

The "it's all about procreation" arguments are just hand-waving rationalisation, the pretence of having an evidentiary argument when all there is is the search for rationalisations to legally support a religious taboo.