It is amazing how Mother Father Baby games start on its own- like a milestone.
Pay attention to a bunch of kids playing in the room and you will hear snatches of conversation
Mother, I am hungry
Mother I am going to school
And more often than not, the one who is the Father, is not playing with the other kids inside the room- he is (tri)cycling outside the confines - like in the living room, or if the "house" is a secluded corner of the building complex then the father will be cycling in the open portion of the complex.
So they pick it up early in life that mothers feed when you are hungry and the father is always outside- in office or somewhere else but not with the kids or the mother!