Be quiet, Louann Brizendine
The problem? Well, first, it's probably not all factual. The Boston Globe has started the critique by pointing out that Brizendine got one of her statistics from self-help rather than science, and that probably won't be the last objection. I haven't read the book, but I'm skeptical of anything that makes cut-and-dried claims about neural functioning and architecture. It's more or less inevitable, at this point in our understanding of the brain, that most such claims will turn out to be exaggerated or at least controversial.
But more importantly, this just isn't the time. It doesn't matter how accurate it is to say "male and female brains have fundamental differences at the physical level" -- and of course it is to some degree accurate, though probably not to the degree Brizendine claims. No matter how many minor differences one finds, on average, between male and female brains, it is not going to have nearly the explanatory power of socialization. The inability to deconstruct, the inability to see how "just the way things are" breaks down to just the way things have been, is a fundamental characteristic of the kind of narrow-minded, selfish, blindered individuals we have running the country right now. This is not the time to encourage this particular brand of ignorance with essentializing pop-sci. What you end up with is a bunch of right-wingers who not only can't deconstruct, but now think they have convenient scientific evidence that says they don't need to.
Remember "those who don't know history are doomed to repeat it"? Those who don't know how history contributes to present attitudes and beliefs are doomed to rule from a soundproofed box of essentialism and prejudice, and we shouldn't be giving them excuses to stay there. Cautious data on the relationship between hormones, chromosomes, neurotransmitters, and brain structures? Sure. Excitable pop-sci aiming to crack the bestseller list by playing into prejudice? Not right now, thanks.