Friedrich Engels analysed Bachofen's views as follows:
(1) That originally man lived in a state of sexual promiscuity, to describe which Bachofen uses the mistaken term "hetaerism";
(2) that such promiscuity excludes any certainty of paternity, and that descent could therefore be reckoned only in the female line, according to mother-right, and that this was originally the case amongst all the peoples of antiquity;
(3) that since women, as mothers, were the only parents of the younger generation that were known with certainty, they held a position of such high respect and honor that it became the foundation, in Bachofen's conception, of a regular rule of women (gynaecocracy);
(4) that the transition to monogamy, where the woman belonged to one man exclusively, involved a violation of a primitive religious law (that is, actually a violation of the traditional right of the other men to this woman), and that in order to expiate this violation or to purchase indulgence for it the woman had to surrender herself for a limited period.
(Friedrich Engels, 1891: see link)