By the age of 18 you are, in the eyes of the law if nowhere else, considered responsible enough to know how to behave sensibly with alcohol. It has to do with health to some extent - a gallon of gin a day is no good for a 6 month old tot.
18 is just a figure plucked from the air, its 21 in the USA and probably less in other countries. Alcohol is a drug and drugs are bad for you if not used in moderation. They figure that by 18 you can recognise what a moderate amount is.... although look in any british city at midnight on a friday and you'd wonder.