The defining characteristic of the family is based on is a contract.
This is true of both human and animal families.
A well-defined relationship exists among family members, which marks their obligations to each other, and it is this mutual obligation that forms the family.
When there is no obligation, there may be a love affair, or a breeding plant—but not a family.
This may seem like a very cold, remote, legalistic, and technical definition of family, but it is realistic and accurate, and this mutual obligation forms the stable basis of the family.
"Contract" is, of course, a human term; it does not apply to animals.
Even among humans, who are able to form contracts, most such agreements are never written, or even expressed explicitly.
Surely, a family formed by two birds or two monkeys is based on nonverbal understandings, basic agreements for mutual interaction, which they nevertheless keep.
On the other hand, even an old-fashioned, written contractual husband-wife relationship may change enormously over time—not only in the course of generations, but even within the life span of the same family.
Yet, as long as it is a mutual agreement that both sides accept and keep, the family remains a family.
All the rest is additional, optional, and not entirely necessary for building and maintaining the basic family structure.
Whatever the family's agreement may be, it is always based on mutual trust.
No family can exist if one of its members is mortally afraid of being harmed by another member.
There are no spider families because female spiders try to devour the males.
On the other hand, two wolves living together are ferocious animals that can harm each other considerably.
The fact that they are a pair means that they have an agreement not to do so, as well as a pact to fight for those things that are for their mutual good—because mutual protection is also part of the family contract.
Thus, without signing any legal papers, when the female bird is hatching the eggs, the male bird feeds it, and in that relationship both partners perform their share of the agreement.
–Rabbi Adin Steinsaltz
From Simple Words by Rabbi Adin Steinsaltz