Property and economics begin to play a larger part in the family, as a pairing family had responsibility for the ownership of specific goods and property. Polygamy is still common amongst men, but no longer amongst women since their fidelity would ensure the child's legitimacy. Women have a superior role in the family as keepers of the household and guardians of legitimacy. The pairing family is the form characteristic of the lower stages of barbarism. However, at this point, when the man died his inheritance was still given to his gens, rather than to his offspring. Engels refers to this economic advantage for men coupled with the woman's lack of rights to lay claim to possessions for herself or her children (who became hers after a separation) as the overthrow of mother-right~~ which was "the world historical defeat of the female sex". For Engels, ownership of property created the first significant division between men and women in which the woman was inferior.
On the monogamous family, Engels writes:
It develops from the pairing family, as we have already shown, during the time of transition from the middle to the higher stage of barbarism. Its final victory is one of the signs of beginning civilization. It is founded on male supremacy for the pronounced purpose of breeding children of indisputable paternal lineage. The latter is required, because these children shall later on inherit the fortune of their father. The monogamous family is distinguished from the pairing family by the far greater durability of wedlock, which can no longer be dissolved at the pleasure of either party. As a rule, it is only the man who can still dissolve it and cast off his wife.
The Origin of the Family, Private Property and the State https://en.wikipedia.org/wiki/The_Origin_of_the_Family,_Private_Property_and_the_State
~~ Primitive communism, according to both Morgan and Engels, was based in the matrilineal clan where women lived with their classificatory sisters – applying the principle that "my sister’s child is my child". Because they lived and worked together, women in these communal households felt strong bonds of solidarity with one another, enabling them when necessary to take action against uncooperative males.