The Chalice and the Blade is a work of great magnitude that argues an alternative view of history, specifically pre-history, as more than a patriarchal and hierarchal series of civilizations. The title use the symbol of the chalice (female) and the blade (male) to contrast -- and perhaps balance -- both forces.
On page 73, Eisler talks about our assumed interpretation of the past and how they affect us today. It's important to understand that the vast majority of historians have been male, and that there are many implicit assumptions about men being in charge and women being bit actors throughout history. The rare female ruler is essentially a woman playing a man's part.
The view of history and public life as male, and the view of the individual as more important than the group, go hand in hand. Female dominated (matriarchal) societies would have functioned based on a spirit of cooperation in which the group was considered first, the individual second.
Our collective beliefs, which continue to this day, are that men hunted and women gathered. Our belief system extends to thinking that primitive societies were similar to our own today, with men in public positions, and women taking supporting roles. This view is so ingrained in human consciousness that it is difficult to see human society as ever having been one in which both men and women contribute equally.
Such a view would also require understanding that cooperation, rather than competition, is the foundation of human civilization.
Eisler attempts to right this by suggesting that gathering, a job done primarily by women, is an important example of a role (in the distant past) that functioned based on cooperation rather than competition.
That the gathering function is equal (or perhaps even more critical) than the hunting function, is fundamentally distinct from our basic, underlying, and unquestioned views about what drives human nature. We tend to see humans as competing with one another to get things done, where cooperation is a less valuable approach to problem solving. We see humans as competing for limited resources; winners get far more because they are more important, and thus should have a higher seat in organizational hierarchies.
Eisler's view also throws doubt onto how practical our current hierarchical, capitalistic, and propertied society is. The triumph of the individual, the ability for a 'lone man' to succeed, and the necessity to reinforce values such as aggression and competitiveness -- all are thrown into doubt once the true nature of humans as cooperative creatures is revealed.
Multiple problems emerge in societies where the individual is celebrated over the group, and many examples can be found in American society. Despite our need to care for each other, our healthcare system rests on the individual having a job. The individual (through an employer) can pay for health insurance, and society doesn't need to contribute. Despite our need for an educated workforce, the individual (or his or her family) must pay for higher education. If the society paid (government funded higher education) it would lead to a better-prepared workforce.
In the US, many assumptions about cooperation being the "second-best" approach to life keep up from solving basic problems of healthcare, poverty, housing, education, and energy usage. The philosophy of "the the victor goes the spoils" doesn't work on a large scale and, as Eisler rightly chronicles, is not really how humans evolved, and not how we prospered.