>The way I see it, it should be modeled as {both-boys, boy-and-girl, both-girls}; by telling me that one of the kids is a boy, you eliminated one possibility out of three, leaving us with 1/2 as an answer.

This would be like saying "When I buy a lottery ticket, the only outcomes are {lose lottery, win lottery}; therefore, I have a 50% chance of winning the lottery."

The difference is that boy-girl is twice as likely to occur of those three choices.