In the first case, I guess what's happening is that when we pick two people randomly with uniform distribution, we expect, with equal probability, any combination of boys and girls: MM MF FF FM. When we observe a girl, we can exclude the case of two boys, so the remaining cases to consider are MF FF FM, where obviously only 1/3 of the cases is two girls.

So I guess what makes this counterintuitive is that we think of the example as independent variables actually affecting each other, but what happens is really that we're drawing from a collection without replacement, and obviously the mix of the collection is going to change as we do so.

This should apply also on a humankind, world-wide scale: if you have met three women in a row, the fourth person you meet is more likely to be a man. Gambler's fallacy! Or just drawing without replacement. A roulette table is drawing with replacement. :)