The reason age was introduced was simply was a way of differentiating the two children (giving them identity). You introduced names to differentiate the two children, which is another perfectly good way to do it.
But then you _also_ introduced age. Because you now have two different ways of labelling the children, you've introduced a new variable, and that changes the probability.
A better way to look at it is with two unisex names: Drew and Sam. This completely replaces the age thing as a way of identifying them, so forget all about age.
Our possibilities are:
Drew: boy, Sam: boy
Drew: boy, Sam: girl
Drew: girl, Sam: boy
Drew: girl, Sam: girl
We know Drew and Sam can't both be girls, because at least one is a boy, so that leaves:
Drew: boy, Sam: boy
Drew: boy, Sam: girl
Drew: girl, Sam: boy
There's a 1/3 chance that both Drew and Sam are boys.
But then you _also_ introduced age. Because you now have two different ways of labelling the children, you've introduced a new variable, and that changes the probability.
A better way to look at it is with two unisex names: Drew and Sam. This completely replaces the age thing as a way of identifying them, so forget all about age.
Our possibilities are:
We know Drew and Sam can't both be girls, because at least one is a boy, so that leaves: There's a 1/3 chance that both Drew and Sam are boys.