The statistic touting men's success rate in seeking custody ignores the price of entry. Men /want/ to be in their children's lives, but must be wealthy to fund a custody battle (while also paying child support and alimony if he was married) in order to do so.
Women are the automatic receivers of custody, it is then the father's "privilege" to hire a family practice lawyer and sue for custody to the tune of thousands of dollars and invasion of his privacy via drug and psychological testing.