From a psychological standpoint family has more of an impact on the growth and development of a child. One could argue that the way a family raises a child comes from the society that family exists in but there is always an outlier to such a claim. Our growth starts in the home, be it good or bad. We may take on our parent's attitudes or opinions or we may do a 180 and try to be the opposite of our family. Parents teach their kids more than anything else just by being near the child and being observed. Society takes effort to impact a child, parenting just takes presence.
Though a more thorough question would be teaches what, the majority of subjects we're educated in comes from society. Sure, your family most likely has taught you a lot of things. In fact, most of the ideologies we have politically, religiously, or morally, stems off the basis of our families' ideologies. Such is political socialization. But i believe that family only sets the foundation for the furthering of ideas since they only expose you to one point of view. The education society provides us with incorporates endless vantages, therefore helping us build upon and contradict our initial beliefs. The more of a topic we are exposed to, the better understanding we will have of said topic. Overall, i believe that society teaches us more than our family does because it covers more ground, and shows us more perspectives.