The question is, who took care of the child before the two split up?
If the mother has done all the child-rearing, and then gets a support order, and then all of a sudden the man wants custody, it's going to look like he just wants out of child support. Similarly, if the man just shows up out of the blue, he's going to have to start with visitation and prove himself.
On the other hand, if the father acted like Mr. Mom before the two split up, he's got a very good shot at custody, split custody, or shared custody.
Most men are satisfied with visitation, at most. Some don't want anything to do with the kid. My guess is that the kids who grow up to be criminals were abandoned by their fathers, and that the dad wasn't much to begin with.
No, the question is, is one parent incapable of taking care of the child?
The burden of proof is on those seeking to diminish a protected right (to parent). Roles assumed during a marriage have little to do with the capability to adapt to a split. Fitness is the only issue between competing parents. The law is well settled, but often abused.
The problem is that he has the burden of proof and is not on equal footing with the "hallowed" mother. Notice your expression for being a good caretaker is "Mr. Mom.
Your guess is worth about what I'm paying for it here on the internet. This data applies equally to mothers who were "abandoned," mothers who don't remember who they spread their legs for, and mothers who voluntarily opted out of that whole icky "man thing."
Even if one were to accept your man hating version of reality at face value, the data is irrefutable - women are generally failures at raising kids alone.