Ah, the glories of the internet. Without it, I would never have found this article linking alcohol consumption with monogamy. After reading the journal article, there is certainly a question as to whether or not alcohol consumption and monogamy have a specious relationship, like storks and babies (there is a positive correlation between stork populations and birth rates in Sweden caused by the fact that storks live in rural areas where the residents have more kids), or a positive correlation. Unfortunately, the authors never really describe why there is a positive correlation between alcohol consumption and monogamy that exists to this day.
So, why is it that alcohol consumption = (at least in theory) monogamy? If I had to speculation, I would say that the reason is beer goggles. That is, the tendency of drunk people to engage in riskier sex than they normally would (and alcohol, we love you for it). This tendency leads to some problems, especially in the area of determining the parentage of the child. Plus, there are some drunken hook-ups that should never be discussed (beer - helping ugly people breed since 1800 b.c.) What's interesting about monogamy is that its a statement that all children born to the wife are assumed to be the children of the husband. All other relationships with other women, under the Roman/Greek version of monogamy, as stated in the article, are strictly informal, and the children produced were considered illegitimate. Problems with beer goggles solved.
As women gained more equality, there was a push to do away with informal polygyny (because, apparently, women don't like it when their men have sex with other women), and we are left with what we have today.
In the more, ahem, sober world, there was no need to worry about spontaneous hook-ups because, well, everyone was sober. So, rather than informalize relationships - to the point of ignoring their existence - these societies formalize them into marriages. The problem is that polygyny is inherently biased towards younger, poorer males - the exact kind of people who tend to do fun things like lead revolts and commit crimes - because they can't compete with older, richer men for mates.
Anyway, for whatever the reason, HOORAY BEER!!!