>The most obvious way to do that is to talk about the older and younger.
Exactly. The father doesn't talk about older and younger, but the table does. What it should look like, because you're correct that age is irrelevant: B (given) * [b|g] -> [Bb|Bg], or if you account for age: [B is first|B is second] * [b|g] -> [Bb|bB|Bg|gB]. But you have to pick one or the other! Either way, it works, but you have to account on both ends, not just one. He's calculating for BG as if age were relevant, but it's not.
The computer "simulation" is wrong because it is grounded in the logic that one child's sex wasn't a given all along, when in fact it was. NB: if you're throwing results out, that's a bad sign.
Yea/nay?
Or, again, you can just step back and say: X is a boy. What is the probability that Y is a boy? Why on earth would it matter what X was? Do you meet 2/3 women because you are a man?