Fathers act as the protectors of their families. And despite the pervasiveness of two-income families, it's fathers who can work without interruption throughout the nine months of pregnancy and the demanding years of a child's infancy to ensure that the family's basic needs are met. A child-support check does not suffice. And, one suspects, Alan Alda models do not suffice either. Single mothers are less effective parents not just because one must do the work of two, but because children need a father's influence and example.
Fathers have more natural authority than mothers.
They are taller, stronger, and louder than women. They are emotionally tougher. And at some very basic level, kids, especially boys, figure out that even very mild fathers are more threatening than mothers. There are moments in the rearing of a child when healthy fear is a necessary thing. Children fear to disappoint either of their parents, of course.