The theory of the family, developed by talcott parsons, argues that nuclear families are necessary for child rearing and fulfilling society's need for productive workers.

The functionalist theory of the family, developed by Talcott Parsons, argues that nuclear families are necessary for child rearing and fulfilling society's need for productive workers.

Explanation:

For functionalism, society can be understood metaphorically as a living organism that is composed of different organs or structures, each of them with a function or functions necessary for the social organism to live. Society is a complex system whose parts "fit together" producing a balance or social stability.

According to the functionalist paradigm, the family meets four basic objectives that make it an essential institution for the proper functioning of a society.

In the first place, the family fulfills the function of socialization of the children, understood as the learning of the basic tools to be well integrated members of society. It is not the only social institution involved in this task, there is also the educational system for example, but the family is essential especially in the first years of the life of individuals, although of course, family socialization continues throughout life.  

Second, the functionalists point out the function of regulating sexual activity. All cultures rationalize sexuality through their matrimonial forms, which can be very different from one society to another, in order to maintain a certain order in the organization of kinship and property rights. A cultural universal related to kinship and sexuality is the incest taboo that is a norm that avoids sexual relations or marriage between relatives and that, despite its universality, acquires different forms.  

The third function is reproduction. The family is the environment in which children are born and this function is vital for society to last. The social identity of the individual defined, among other characteristics, by ethnicity, religion and social class is determined by birth in the context of a particular family. The socioeconomic position at the origin is marked by the family.

And finally, the functionalists say that before a hostile outside world, the family provides material and emotional security. The individual seeks physical protection, emotional support and financial assistance from close relatives and, to a greater or lesser extent, almost all families provide this assistance, which does not mean that there are no economic conflicts and difficult relationships within them.

answer; john stuart mill's principle of utility is your answer; /// good luck