I believe I understand the standard argument that says that one should put an equal effort in reproducing male and female offspring. But the standard argument only seems to apply to the population as a whole. That is, there is no reason why half of all breeding couples shouldn't produce males and the other half females. Thus, if the standard argument was all that was going on, I would NOT expect to see the detailed balance we have where the probability that their next child would be male/female was very close to 50% for all couples. I would NOT expect very nearly 1/8 of all three child couples to have only girls. As far as I know (which isn't very far) this IS true for all higher animals. Why?
PLEASE NOTE: In elementary math classes, it is frequently hard to convince a student that his proof is incorrect when the theorem is true. I think this is the situation here. I think the standard argument incomplete, but its incompleteness is ignored because it gives the right answer. This is meant to be a brief technical question. A reference is a valid answer.
Your fault -- core dumped