Yes, I heard about matrilineal and about more egalitarian cultures (than patriarchy), considered to have been, somehow, "matriarchal":
whereas, in matrifocal families, patriarchal systems can still prevail:
But opinions differ much. The "Chalice and the Blade" is interesting, and I missed out quite a few excellent reads, as in these times, I was focusing on work-related technological, scientific and biological domains, languages, etc. And although literature in English is widespread, our bookshops sell their translations in our own languages, i.e. our book-shops must order original versions in English, which involved waiting times of about one week or more (it was before the on-line access for everybody).
And there were all these congresses ...
The egalitarian systems show that they can reduce aggressivity and violence, but they also leave too many opportunities for less scrupulous "elements" and for aggressions by other, profit-oriented or hostile systems - whether from inside or outside. Sadly enough, "opportunity makes the thief".
The "good example" will not be followed automatically by everybody, and also in egalitarian systems, rules and responsibilities need to be clearly defined and supervised, and every society has its more or less ruthless wrongdoers.
Furthermore, mentalities, beliefs, attitudes, resentments, grudges, as well as educational and personal background impregnation cannot be changed or evolve from one day to the other.
And we cannot "love or hate on command".