What is the sociological definition of a family?

The family is responsible for producing new members

Question: What is the sociological definition of a family?
Position‹2 of 6›: Family means a shared residence, economic cooperation, and reproduction
Argument‹4 of 4: The family is responsible for producing new members

Families create new family members through procreation. Producing offspring is a fundamental necessity for life, and the family fulfills the role of procreation, raising children, and furthering human life for generations.

The argument

Producing offspring is a fundamental necessity for life. A species must be able to reproduce in order to survive. Moreover, a species must reproduce with genetic variation to most successfully survive. Human genetics are finite. The only way to pass down genetics, characteristics, phenotypes, or other hereditary traits is to have children. Families have a duty to continue their family name by producing offspring. Giving birth to children brings value to the world. Valuable people (having special genetic features) produce offspring with similar valuable genetic traits. In addition, the creation of life itself is the most valuable characteristic of life. One’s progeny “carries its share in society” for future generations to benefit. Families have a duty to produce offspring. Procreation is not only a defining characteristic of a family but of life in general.

Context

Family heritages can be traced for generations and connect to a broader name or identity. Families have a responsibility to continue their family name through their posterity.

Premises

[P1]A species must reproduce to survive, and for humans the only way to pass on genetic traits is to have children. [P2] Families therefore have a duty to continue by producing offspring who carry their share in society for future generations. [P3] The creation of life is itself the most valuable characteristic of life. [C] Therefore, because the family is responsible for producing new members, reproduction is part of what defines a family — a shared residence, economic cooperation, and reproduction.

Counter-arguments

Families can still make an impact on society without leaving offspring. Some families may not be able to have children, have financial limitations, or may choose to not have children. For example, Mother Teresa and Sir Isaac Newton both bettered humanity with their respective contributions, all without starting a family or leaving offspring. They still left a valuable impact—albeit not children—on society for generations to come. In addition, humans can procreate without being a part of a family. People can choose to have a child in traditional means, yet not start a family. Similarly, mothers can give birth to a child with other means (such as a sperm bank) but still choose to not form a family.

Rejecting the premises

[Rejecting P1] The premise moves from a species to a household. Humanity's reproduction does not require any particular family to reproduce, so a definitional claim about families cannot rest on a biological necessity that operates at the level of a population. [Rejecting P2] The duty is asserted rather than argued, and it does not follow from what precedes it: the counter names people who contributed to society without children, and couples who cannot or choose not to have them are not thereby less a family. [Rejecting P3] Ranking people by "special genetic features" is not a claim about what a family is and has no place in a definition. The argument also runs the wrong way for its position, since people procreate outside families and form families without procreating — so reproduction cannot be a defining condition.