His point is that a person telling you they have one girl would be accepted as referring to a particular child. Thus, BG and GB merge and the odds are 50% of a boy and a girl.
Pedantically, they don't merge, you just rule out GB or BG. So, initial conditions:
1) X: G, Y: G
2) X: G, Y: B
3) X: B, Y: G
4) X: B, Y: B
If you are told, "at least one is a girl," as in the posted question, you can only rule out case (4). If you are told more specifically that X is a girl, you can rule out (3) and (4), giving the 50-50 chance.
Which still seems a little weird to me, that knowing which is a girl, regardless of which one you know about, changes the chances.
Which still seems a little weird to me, that knowing which is a girl, regardless of which one you know about, changes the chances.