Women get custody 85% of the time with most of the rest being women that don’t want the kids. 97% of alimony recipients are women (despite higher earner 35% of time). The legal cost for a man to even attempt to get full custody is at least 20k and you still win a small minority of the time
It’s the large earners who insist that the woman stay home with the kids who then try to take the kids away if there is a divorce, let’s say when he gets his secretary pregnant and wants to move on. There are special divorce lawyers who only handle contested divorces from professional men who try to destroy the mother of their children pursuant to divorce. Men who can well afford the $20K. I know of women who have paid up to $80K just to keep partial custody of their only child from men like this.