This might be better suited for ask anthropology, I'll post this there if that's the case. Beyond a few cultures I know of, and the ones I know of tend to be a bit more on the fringe, why was inheritance always based on who the father was? It's pretty hard to contest who the mother is, but not so much with father's. Wouldnt it just be easier to pass that stuff down the mothers family line? I would think it would avoid a lot of controversy.
X-post would be a good idea.
The dominant model tends to be patrilineality, but there have been many bilineal cultures, like America, and certainly matrilineal ones. The Pharaonic throne was matrilineal - no question but outside of conquest it passed mother to child.
Herodotus tells us the Carians were matrilineal, and used matronyms rather than patronyms. He ought to know as he was Carian born and raised. They also had queens regnant, like Artemisia of Helikarnassus, who left her grown son as regent while she went to war with Xerxes.
Medieval Basques were matrilineal.
And as my DH dug up recently, some very few British titles were created to pass from mother to daughter.