The reason women are so good at what they do is because of their oranisational skills. They cook, clean, look after kids etc so much better than men because they are hard-wired to do these sort of things. Men are better at the physical things that women have trouble with, like hard physical sports, hunting, construction work, and general heavy labour. The big problem is, women have been underrated and undervalued by men for their homecare and what they do best, but it's the wankers like Greer and her ilk that are to blame for that. Equality is one thing, but trying to emasculate the other sex just to propagate some bullshit notion of superiority is something else entirely. Greer should have been fucked and burned.
Those are generalizations. --Not that generalizations need be wholly untrue, but it's definitely not like that for every woman or every man. The gender of the brain is a full continuum; sexual differentiation of the brain is based upon the levels of blood androgens which, after crossing the blood-brain barrier, aromatise into estrogen (largely estradiol). It's the estrogens which stimulate neurons which have various estrogen receptors (e.g., ER-alpha and ER-beta), keeping these cells from going through apoptosis. In males, it is the continued activation of these neurons via estrogen during specific times of foetal and early postnatal development that causes this "wiring" you speak of. In females, due to lower levels of androgens (and hence estrogens in the central nervous system) these neurons' growth is inhibited, sometimes to the point of cellular death depending on the local area.
The thing is, the levels of androgens present aren't an all-or-nothing-at-all variable: it's a true gradient. Hence there are men who indeed have brains which process in more the female-typical way, and some women's brains which do the opposite. All because of how much androgen was present in utero. And androgens are able to cross the placental barrier, so if the mother has higher androgen levels in her blood (which can frequently occur with conditions like Polycystic Ovarian Syndrome which is currently diagnosed in about 5-10% of the female population and is the biggest reason for female infertility) the baby will also receive higher levels of androgens and develop more male-typical cognition. Unsurprisingly, butch lesbians have been reported to have been exposed to higher levels of androgens in utero, and women with Gender Identity Disorder, according to the DSM, express higher rates of Polycystic Ovarian Syndrome.
And it's not just early development that causes the sexual differentiation of the brain, but then the switch where, starting puberty, females have higher levels of estrogens than males. This effects neural plasticity (estrogens promote growth, in part due to their close ties with insulin-like growth factor-1, a hormone integral to cellular growth) and estrogen can frequently have an excitatory effect on select neurons, thereby increasing neural activity.
Anyways, sorry for going on, this is currently what my research is getting into. But the point is: I don't necessarily disagree with you that there are general underlying neurological/cognitive differences between males and females, but that it is strictly a generalization and there are minorities of both males and females who do not follow those patterns. It's a typical bell curve, with most men and women falling in the average range, but a bell curve in which the minority tails are also very well represented.
Long story short, you're generalizing too much.