Exchange theory dictates that all relationships can be measured by the giving and receiving of goods or services. This can be applied to the sociological definition of a family.
A familial relationship is one where care is exchanged between family members. Parents care for children while they are young and in exchange, the child will care for the parent in its old age. This transaction is at the heart of the family dynamic and defines familial relationships. Parents also have a similar contractual exchange between each other.
To reduce familial relationships to an exchange of care is too restrictive. When wealthy parents pay others to care for their children while they work, are they negating on this exchange of services? Would this mean that they no longer have a parent/child relationship with their offspring? Few would argue that this "outsourcing" of child care would lead to an erosion of legitimacy in the family unit any more than putting an elderly family member into a nursing home does.
[P1] The parent cares for a child when it is young in exchange for the child's care when the parent becomes old. [P2] This transactional exchange defines the relationship between parent and child.
Rejecting the premises
[Rejecting P2] This definition excludes parents that use child care services to help care for their children or adults that put their parents in nursing homes.