I think (personally, based on my own anthropology reading) that it was the *kind* of society which formed that made the difference. In chimp and gorilla groups, there's no nuclear family. Males may "own" a group but there's no real individual loyalty to one female & her offspring.
At some point proto-hominids transitioned to people (probably 150,000 or so years ago.) It may have been something so simple as pair-bonding between male and female, with the male being *responsible* for the female and her offspring.
One thing you can say for sure about *modern* primitive hunters is that the men don't hunt in a "vacuum." Even though the women don't hunt, they have huge jobs to fulfill - like taking care of the camps, processing the kill, preserving the meat, doing all the sewing and preparing of hides, as well as a good portion of the artwork (decorating hides.) So development of the brain occurred in *both* sexes, without the gross sexual differences in size and behavior seen in the great apes.
This situation is optimal for language development. Males "needed" language to work cooperatively with other men; to persuade a woman to set up a partnership (marriage) with him. Females "needed" language to pass their arts on to other females; to bond with their mates and probably most important - as a means of better raising infants. At some point the survival value of being *talked to* and *communicated with* as an infant had to be phenomenal.
Much like certain segments of our 'society' today....