The COO of Facebook (FB), Sheryl Sandberg, has published a new book called "Lean In."

The book offers career advice for women in a world that is still dominated by men.

Sandberg argues that women need to be more assertive in their careers, fighting against societal programming that conditions them to defer to men, scale back their ambitions, and essentially give up early.

This passivity, Sandberg argues, is the real reason there are so few women in positions of power.

In the context of this message, Sandberg notes that it is impossible to "have it all" as a woman--full career and full home life--if you're also expected to do all of the housework and child care at home.

Related: Mrs. Moneypenny's Career Advice for Ambitious Women

This is why a woman's most important career decision, Sandberg says, is who you marry.

(Sandberg also says the men who do more housework have more sex, an assertion that would be encouraging to those in "egalitarian" marriages in which men do their share of the cooking, cleaning, child-rearing, and so forth. Unfortunately, a recent study actually refutes this).

Sandberg's book has already stirred the pot.

Many women have been offended by Sandberg's implication that they're responsible for their own relative lack of success. As a billionaire, they say, Sandberg is not in a position to speak for normal women.

Many men, meanwhile, have reacted to Sandberg's message by lashing out at her. Sandberg, they say, doesn't deserve her own success and has no business telling other people how to act!

Interestingly, Sandberg herself predicted this reaction.

When explaining why she decided to write this book, Sandberg cites many facts that illustrate why and how women hinder their own progress in the workplace. One of these facts is a study showing that, when men get more successful, people like them more. But the more successful a woman is, the less people like her.

That's a depressing fact. And, unfortunately, Sandberg's own experience would seem to confirm it.

Sandberg has become one of the most successful and powerful women in the world. And now, after writing a book that does little more than urge women to believe in themselves and be more assertive in their careers, Sandberg is being pilloried for a litany of perceived sins.

Related: How to Be a "Superachiever"

For example, people have accused Sandberg of "just riding Mark Zuckerberg's coattails" at Facebook--as if her own hard work and success at Facebook, Google, the Treasury Department, McKinsey, the World Bank, and Harvard doesn't give her the authority to speak about how to succeed.