One of the peculiar features of history is that time always erodes advantage. Every invention sooner or later leads to a counter-invention. Every success contains the seeds of its own overthrow.
We use our intellects not to solve practical problems, but to outwit each other. Deceiving people, detecting deceit, understanding people's motives, manipulating people – these are what the intellect is used for. So what matters is not how clever and crafty you are, but how much cleverer and craftier than other people. The value of intellect is infinite. Selection within the species is always going to be more important than selection between the species.
Sex is about disease. It is used to combat the threat from parasites. Organisms need sex to keep their genes one step ahead of their parasites. Men are not redundant after all; they are woman's insurance policy against her children being wiped out by influenza and smallpox (if that is a consolation). Women add sperm to their eggs because if they did not, the resulting babies would be identically vulnerable to the first parasite that picked their genetic lock.
A son is a high-risk-high-reward reproductive option compared to a daughter.
So you should have sons if you have reason to think they will do well and daughters if you have reason to think they will do poorly – relative to others in the population.
So human society, like ape society but unlike most monkey society, is a female-exogamous patriarchy and sons inherit their father's (or mother's) status more than daughters inherit their parents' status. Therefore, says Trivers–Willard, it would pay high-ranking fathers, or dominant women, or both, to have sons and subordinates to have daughters.
The sex ratio of the population as a whole will always revert to one to one, however biased it becomes in one part of the population, because if it strays from that it will pay somebody to have more of the rare gender.
The sex that invests most in rearing the young – by carrying a foetus for nine months in its belly, for example – is the sex that makes least marginal profit from an extra mating. The sex that invests least has time to spare to seek other mates. Therefore, broadly speaking, males invest less and seek quantity of mates, while females invest more and seek quality of mates.
Behaviour itself is rarely what has evolved; it is the underlying psychological attitude that evolves, and modern women possess a mental mechanism, evolved during the Pleistocene, that enables them to read what correlates to status among men and find such clues desirable. In a sense, both are saying the same thing. Women are impressed by signals of status, whatever those specific symbols are. Presumably, at some point they learn the association between BMWs and wealth: it is not a difficult equation to solve.