court systems
The maternal advantage in family court is misunderstood. The vast majority of custody agreements are negotiated between the parents. So while there is a societal pressure to favor mothers, this is mostly a phenomena of parents hewing to that norm and not the government imposing it from above.
It may be true that a divorced mother or a lady felon enjoy some benefit from patriarchal ideals and norms. This is far outweighed by the harm patriarchy does to women (and men).
If you look at the “nurturing mother” norm in our legal system holistically, I think you’ll find that it burdens mothers with extra duties and responsibilities while stripping them of rights.
I feel like its safe (adjacent) to say that everyone is hurt, and the comparison of those hurts is counterproductive.
In cases where parental agreements aren’t worked out, a bias toward the mother is unfair. Any added burden to mothers while stripping them of rights is also not ok. To take it to a huge extreme: both men and women get raped. Men are mocked if they come forward and women are dismissed or worse. These are both wrong things. Deciding which is more wrong is distracting from the actual wrong thing: the fact that they were harmed in the first place and the authorities don’t take them seriously.