Explanation: Most (though not all!) Ancient Greek polities were... frighteningly sexist, even by the low standards of pre-modern societies.

The Romans were certainly sexist by modern standards, but were relatively mild in their sexism by contemporary (and, unfortunately, many subsequent*) civilizations of the region. A large part of this is the cultural emphasis Romans placed on parenthood.

As means of demonstration, it was common in Greek societies for mothers to pass into the power of their sons, once their husband died. Their eldest son, after all, is the man of the house now, and the man of the house makes the decisions for all the women under his roof! In Athens, the 'jewel' of Ancient Greek democracy, women could not go out in public unveiled, or without male accompaniment. The quote featured is also a... distinctive display of Ancient Greek sexism.

Such a position for Romans, on the other hand, would have been nearly unthinkable! CHILDREN having AUTHORITY over their PARENTS!? What's next, dogs and cats living together; mass hysteria!? Even under the oldest, most sexist, and least common form of Roman marriage, a widow would remain independent after her husband's death. Romans were always expected to pay the utmost respect to both of their parents, regardless of the fact that women (who were recognized as cives sine suffragio - 'citizens without the vote') could not vote or hold political office. Women could, and were expected to be, major participants in public life, and have numerous occasions on which they agitated in the streets or made demands of even the Senate itself (and popular assemblies) in support of women's causes - often successfully. For how could a respectable Roman man just DISREGARD the mothers of the nation!?

On top of this, Roman women could and did manage significant economic assets (to the point that gifts from a wife to a husband - or vice-versa - were not legally recognized as valid, and would remain the woman's property), and would develop the right to divorce freely, remaining independent (sui iuris) even if their father was still alive - a right even Roman men did not enjoy (who would be subject to their father's authority for as long as he was alive and sane). Roman mothers received additional privileges (albeit still not nearly equivalent to participation in the fucking government) such as exemption from taxation and positions of honor at public functions.

The Historia Augusta is a late and unreliable source, but reflects very real Roman cultural norms when it claims an Emperor to have rebuked a unfilial Roman legionary with, "If you do not recognize [respect] your own mother, I do not recognize you as a Roman citizen."

*women could not divorce of their own volition or own property until the 19th century AD in many post-Roman European cultures. Including European-derived cultures like the USA. The past is a BARBAROUS place

Worth noting that Sparta was the unexpected exception to this. Because inheretance was usually split evenly and their men tended to die a lot, a huge amount of wealth was owned by a small number of heiresses.