There is nothing that quite smacks of the power of patriarchy as patrilineal mapping. That is, giving children the surname of their father rather than their mother. What were our fore-fathers thinking? Hmmm…"for fathers." Perhaps that explains exactly what they were thinking. Men were looking after their own interests while matrilineal mapping would have been a much safer bet for knowing the lineage of a child.
The royal families are a varied lot, and I am willing to bet that there are a fair number of queens that gave birth to children whose sire was not the Sire.
I daresay that the emergence of DNA evidence in recent times will do much to undo any idealistic notion of patriarchal lineage. I imagine finding out that the patriarchal lines of monarchy are a lot patchier than history and the hegemony would have us believe.
If we had chosen matrilineal mapping, we could have known with certainty at least one side of our ancestry. Instead, we chose the one side that we could never know with certainty, tracing parentage through the father.
So, men may have the power in saying who is the father in official terms, but in real terms, the truth about parentage lies almost entirely with the mother. It is this parental certainty that gives her, not him, a strong degree of control over reproduction. She holds the power in her hands, or more specifically, in her womb. From conception through to lactation, it is the woman that says what will and will not happen.
The man? It seems that he is just along for the ride.
For all the advantages that there might be to being a man, a man cannot give birth to a baby. Ok, yes, it is acknowledged that Thomas Beatie is an exception having produced two children to date. However, it must be admitted that this exception most decidedly establishes the rule. Thomas was originally named Tracey. He was born as a girl. She decided to have gender reassignment surgery and is now officially a man.
With Thomas Beatie having birthed two children, there clearly is some distinction between 'official' and 'reality' that is yet to be clarified. Just as we need to clarify the real vs official parentage presented the royal and non-royal lineages.
The reality is that men and women are not equal. Officially men dominate women by giving his name to their offspring. However, the reality of parentage is quite different. That men might have an advantage over women in reproduction is about as funny as a sketch from Monty Python.