It has been documented in some species (particularly some mammals) that the specifics of the nurturing behavior need to be learned but, in the overwhelming majority of animals which provide care to their young, it is the female who provides the primary or sole care for them. Sure, exception exist (eg: seahorses, Egyptian mouthbreeders) where the male has an extensive role.
But, in humans, I honestly think the natural behavior is evolving in the other direction - the female is learning, due to our innate intelligence and adaptability, that she does not need to be the primary nurturer.
I think the word 'natural' allows for taught behavior to some extent; it's not the same as a genetic or instinctual trait. Perhaps we're just using the same word in slightly different manners.