The term family is bandied about constantly, in references so divergent as people lavishing love on kept animals to suicide cult leaders enslaving captives to their will. If we were to honor the massive range of relationships that are commonly misdefined as family, there would be no point in the use of the word - there could be no particular identifying and unifying characteristic. I will make a somewhat more narrow definition and reject all others: a family is an autonomous group that includes a man and a woman joined by marriage, the children born to that married couple, and other children adopted by that couple. For the purposes of this text, when the word "family" is used, this is the composition intended and no other.
I am perfectly happy to offend other groupings that demand the title "family", such as "blended" households from re-marriages, same-sex couples that adopt children, multigenerational conglomerations ruled by powerful elders, or others. I have little doubt that some people find great joy and satisfaction from associating and perhaps cohabiting with groups outside of their own nuclear family, but my purpose is not to somehow equate family only with happiness or affinity or sociality. For good or ill, the family simply is what it is - each person has one father and one mother and likely siblings (natural or adoptive) with that same father and mother.
This, in no way, is meant to take away from the ligitimacy of other groups. It is perfectly honest to say that gangs, tribes, villages, ideologies, clubs, collectives, households, clans, races, crews, and kinfolk, among thousands of other associations, can be just as fulfilling or moreso in the lives of individuals than their own family. These other groups or institutions may attempt to put themselves in the role of a substitute for family. Individuals may work to replace their families with such associations in one way or another. No matter how much better such groups may be in addressing individual needs and desires, they still are not a family.
I define the family as I do because this is my understanding of the way God sees the family. Parents are responsible for their children's needs and conduct until they are mature (often interpreted as of marrigable age). Children are commanded to obey their parents until maturity and to bring their parents honor throughout their lives. God's commands presuppose the structure of family that I defined and there is little room for various "redefinitions". Parents cannot eliminate their responsibilities to children through divorce or abandonment; neither can children choose up new "parents" at will and more to their liking. Both of these violations in the sight of God fall short of the greater sin of avoiding or abandoning a marriage covenant where parents model a good marriage and children follow this pattern into their own marriages and families.
Although circumstances such as death may necessitate living outside of a family, this does not negate the responsibilities of parents to their children or children honoring their parents. God blesses subsequent marriages and households and widowed parents raising children alone alongside families in supporting each affected person. Conversely, living puposefully in defiance of God's definition of marriage and family or encouraging others to so live is a most serious split with God's purpose for mortality. God is not kind to those who thwart his work.
To look at God's perspective another way, if a child lacks for the necessities of life, God will turn to the child's natural father and exact vengence on him, no matter the machinations of courts or other earthly arrangements. If an estranged adult child neglects their failing mother who calls for them, God may see this as dishonor for all the parental care given to that child when young and serve up a stiff punishment for ignoring one of the basic commandments. It doesn't matter if we have collected other, perhaps furry, "children" that we prefer or answer with deference to some "second" parent that showed us kindness - our familial responsibility in God's eyes is to our authentic family, not some other construct.
It is vitally important that we understand Godly definitions of father, mother, child, and family. These are the terms used by God in relation to blessings offered to help meet family responsibilities and in relation to punishments meted out for shirking those responsibilties. We are foolish to try to re-define "family" in any fashion that confuses God's definition and his commandments tied exclusively to family roles. We cannot simply delegate these God-given roles to others, substitute governments and institutions for parents, or shirk duties to children because other activities or associations may be more pleasant. Though society can behave as if the nuclear family is irrelevant, God will hold each of us to account for our required contribution to the lives of our parents, siblings, and children.