Excepting the case where the father is an abuser, the male figure in most modern families still is capable of earning more money, having a more stable job, and supporting themselves. It stands to reason that a child in a custody case should be given custody to whichever parent is more responsible and has more control of their finances and lifestyle. When, as is usually the case, the father has a stable job and income, they have more experience managing multiple areas of life, and would be better suited to take care of the child in a custody case.
Studies show that, EVEN WHEN CONTROLLING FOR SOCIO-ECONOMIC DIFFERENCES, single fathers are actually better parents than single mothers all around.
On the other hand, single mothers often (but not always) coddle their children far too much and lack the disciplining and stern guidance a father is capable of. Thus you have immensely higher rates of violent crimes (ie assault, violent theft, rape) in youths coming from single-mother households vs single father and two-parent households.
My opinion is that is solely depends on the nature of the parent. Not all mothers are "motherly" and not all fathers are "fatherly", as was the case for my parents. However, most mothers do fall under this nurturing, caring image we think of. When you talk to the parents of a mentally or physically disabled child, the mother will often speak highly of their kid and say things along the lines of "he's such a special boy, he can do anything he wants if he puts his mind to it!" whilst the father will be more realistic and less optimistic. Anecdotal evidence aside however, it seems that the stats are greatly against single mothers.
Speaking very, very generally, it's the mother who is better ready to take custody of children. I realize that it's a stereotype and things are changing and all that, but nevertheless, at this point in time it's still the mother who recognizes that it's real work and that you will have to give up your nights out and sleeping in and whatever else you like to do. There are still too many men (and yes, some women) who think that work done at home for no pay isn't actually work or that it's something that can be handed off to someone else.
It is my opinion that mothers are more fit to take custody of their children than fathers in custody cases. I feel that the mother is more likely the parent that children are emotionally attached to, and would be a better mother to those children than the other parent could be a father to them.
I actually do not think that either mothers or fathers are better fit to take children into custody in cases. I think that each situation is different. And people in such cases shouldn't be judged because they happen to be a mother or father. I think that people should treat each case differently.