I read that and it seems wrong. The question asked "what fraction of the pop is female" but his argument is that 3 families of 4 girls and 1 family of 12 boys make the fraction of girls in the average family 75% (the average of 100% x3 and 0% x1) which is non-sensical to me.

>E[X]/E[Y] = E[X/Y] is not a valid identity.

is completely irrelevant here because it is being used to point out that a non-answer is wrong.