I hadn't seen the comments on the article, thanks for pointing them out. That's a pretty impressive readership.

I had seen Steve's comment, but I disagree with him that 1/2 is the solution that requires a contrived understanding of the puzzle. The 1/3 solution is only valid if we know he will preferentially reveal a male child over a female.

Imagine Steve wants to pose this puzzle. He has two children. There is a 25% chance he has two boys, so he would be forced to say "...one of them is a boy...". There is a 25% chance he has two girls, in which case he must say "...one of them is a girl...". There is a 50% chance that he has both a boy and a girl, in which case he can pick either variation of the puzzle.

We heard him use the male version. If we know he would always choose the male version when given a choice, the answer would be 1/3. If we know he would prefer the female version, he must have two boys. If he has no known bias towards one or the other, we gain no additional knowledge, and the probability remains 1/2.