The reality is women overwhelmingly get sole custody of the children. This study cannot draw conclusions as to the reasons for the disparity. Followup interviews with attorneys and mediators provided many differing opinions. That's the way it's always been. Women are really better parents.
Men tend to ignore and abuse their children.
Giving women custody is a way to rationalize giving women more money after a divorce. Men don't really want their children. Judges are sexist. The system is dominated by staff evaluators. Giving women the children means simpler paperwork for the courts.