Once a month is pretty mild. Depending on the society, is only a little beyond what's normal. From my experience, an average college student in Ireland might expect to binge drink twice a week, on Thursdays and Saturdays; on Thursdays with your fellow students because it's the last night of the week before a lot of people go home for the weekend (it's a small country), and on Saturday with your friends at home.

I say average, because what we'd want to call alcoholism would go further than what's normal in the society; it would need to be drinking to excess to escape your life, and ending up with other problems, like being kicked out of places, waking up in strange places (possibly with strange people), not remembering the details of the night before until you piece it all together out of fragmentary memories, passing out in parties, pubs, clubs etc. These are a couple of stages beyond mere "binge drinking".