The problem really isn't a set age limit, the problem is any culture that encourages and glorifies binge drinking and also because you need to hide drinking under a certain age because it's illegal. Yet you do need to set a standard for a society to agree upon.
That being said, the other ages of consent are nominally around 18 for voting, marrying, service in the military, etc. So it should be a standard that applies for all of the abilities to act in a responsible manor without "parental" supervision.
Yet we're beginning to understand that human brain development isn't really completed until around age 25. Really grasping accountability for your actions and reigning in childlike impulse behavior. But I've met 14 year old's with more understanding of adult concepts and who act and behave that way, than some 45 year old people who still act childishly.
Not keeping a childlike sense of wonder into adult life (which is great); but greedy, selfish, rude and uncivil behavior, no comprehension of responsibility or understanding of the repercussions for your actions. This is the drag and hindrance to human societies, and necessitates the need for the setting of these 'arbitrary' age limits in the first place; but because each individual is different, actually individually determining what a persons current level of responsibility - is currently out of our societal abilities.