"Necessarily" is a strawman. I'd speak of probability, not necessity since our evidence of prehistoric human life is scarce.

But just look at the biological differences in body types. Women are given milk-producing breasts and fat stores to manage the carrying of infants in their wombs. Men have none of that. So men had to find other functions to make themselves useful. Evidently, they put themselves in harm's way, to provide the clan meat and to protect the local people from predators and rivals. Thus, men are more likely to be muscular than women. Those are biological differences that have nothing to do with a patriarchal ideology. On the contrary, those differences (the biological division of labour) preceded the patriarchal rationales.