This is an interesting article, pondering the smaller brain size of women compared to men (women's brains are on average 100g lighter).
The answer to this problem, it's postulated, may be found in research into foxes. Over a period of fifty years a Russian scientist bred foxes, aiming to turn the wild creatures he began with into domesticated animals. In each generation he selected the pups which were most friendly to humans, gradually taming them. After 35 generations (equivalent to the 10,000 years it took early man to domesticate wild wolves) he ended up with this: "tamed foxes wagged their tails, whined for affection, were submissive, barked like dogs and their ears flopped."
One aspect of this domestication procedure is that the brains of the tame, floppy eared foxes were smaller than their wild counterparts.
Domestic animals generally do have small brains. On average, domestic dog, cat, sheep and pig brains weigh 25 per cent less than those of wild animals. The mechanism remains a mystery.
The theory is that over time men may have "domesticated" women (and I use the term loosely- I know all too well that these supposedly tame creatures can suddenly and without warning revert back to a wild state), by selecting the friendliest "tamest" of the fairer sex to mate with. Women in turn may have selected for more assertive males.
Another aspect of this is that the smaller brain size is associated with a greater emotional intelligence, the tame foxes are much more adept at picking up on emotional cues from humans than their wilder, bigger brained relatives.
Or it could simply be that women have smaller brains because they are generally smaller than men, and brain size and body size are linked.
Whatever the case turns out to be, the "foxy lady" theory is food for thought.