That's more likely the difference. If men are by dafault the better parent, where are they?

Courts aren't favoring mothers. They are favoring consistency and the best interest of the child. They look at who's going to be less likely to bail and who was already the primary caregiver. That's the standard, because it's provides stability for the child during a turbulent time and the courts don't want to flood the state with kids to take care of if they award custody to the father and the father then bails when things get tough.

Personally, I think the best parents are the ones who wanted to be parents. They're the ones that go all in and aren't resentful, regretful parents. Gender doesn't matter.