The proponent of exclusive custodial control must prove the other parent's unfitness for custody. This is easy, if say, the other parent is a convict or a drug dealer. It's not so easy for suburbanites or rich folk. While the bar is lower than criminal guilt, it's not much lower -- proof must be by "clear and convincing evidence", which is significantly higher than the usual civil burden of "more likely than not".
Indeed, in over 90% of the cases I worked on, the exclusive custody proponent lost. The myth about mothers always getting the children isn't just a myth, it's blatantly untrue. Where exclusive custody is awarded, the father is just as likely to get custody of the children (usually b/c the mother does not have a job and is unable or unwilling to find one).
Kid, I worked in Cleveland. If there's any city where mothers should be "stealing" the kids from their fathers, its going to be a city where more than a 1/3rd of the male population doesn't have a job.