Actually, before the fifteenth century beer was brewed without hops, and so was brewed often. Everyone drank very strong beer with their meals, and even the children drank beer. However, the children weren't given the same beer as the adults, but instead had a 'small beer', which was less alcoholic - Which is where the saying comes from, similar to child's play.

The irony is of course, that even the small beer consumed by the kids was more alcoholic than full strength (around 5%) beer today.