“But women get unfair advantages in custody battles”

handaxe:

FALSE. Fathers who ask for sole custody are far more likely to get it. It’s just that they don’t ask, mostly women do. Men win custody over women even if they are ostensibly unfit. More and more, judges and parents rule in favor of 50/50 custody. In fact, in the past ten years, the men’s rights movement has been devastating to women seeking custody in court and women are awarded sole custody about half as many times as men.  

So find a new fucking myth.