When searching around, the sites you find that exist for helping out dads are substantial. Real hardship, current stories, and dealing with the grief of having your kids taken away by a woman who has gotten tired of being married.
When divorce happens, that's when you see what people are really made of. Some women will take custody just to hurt dad.
Anyway, I hope you're right about the lessening of gender bias. I'd love to see data. No idea where I'd find such data though.
Also look up alien abduction, underpants gnomes, and other urban legends.
I don't claim that courts in the past favored mothers, but in the present, there is no gender bias under the law.