In Catholicism the answer is at Confirmation. That is when the teen has decided to affirm for his or herself that they really believe in the Church's teachings. The effective result in society, however, is that children become adults when they leave their parents to go to college because until then the parents are really making many decisions for the child.
The notion of childlike innocence implies a much younger age than when people effectively become adults. This innocence takes on the understanding that children are too young to discern or understand or consent to most sins and thus commit few.
And that's why I don't like the idea of Confirmation. It wouldn't be so bad if it was at an older age, but mine was at 13, and I understand Catholic ones are about the same age. No kid at that age can truly claim that and know it. What percentage of my Confirmation class are Lutheran today? I'd estimate that about 25% aren't Christian at all, another 25% are some other type of Christian, and another 25% are really half-assed barely practicing Lutherans. Catholic confirmations from the same time as mine probably have similar numbers.
