Family is a social construct and it appears that all cultures, ethnicities, and nations practice family and talk about Family in different ways.
As a psychotherapist who has studied Family Systems, I agree that our families and childhoods are crucial factors that influence our psyche and development. And by "our" I mean beings (humans, animals, all living beings). It is obvious that how one is born (including what occurs prenatally), how one is raised, and with whom, will influence one's sense of self, direction, and future.
Still, this does not make me, personally, value the Family. Although I can recognize the Family as a very important aspect of society-- historically, psychologically, and economically, it does not invigorate me with a desire to make a family, in the traditional sense, for my self.
Growing up in a family that was not very emotionally attached, I believe that influenced me to think about family critically. As I have insinuated, how one is defining family is very important, before asking if one values it. When I say I do not value the Family, I am describing the white-american family values that I have been born into, and have socially learned as a United States citizen. The conventional view of an American family--wife, partner, child, settled down in a suburb or somewhere they can afford (since having a family is expensive); these are the things I do not value highly or want for my life.
But, if we are defining family as a biological connection to someone, then we all are all born into a "family." An amazing woman gave birth to you! Maybe she gave you up for adoption, raised you alone, with a partner, or your biological father, or had help with public assistance, either way, you are someone's child and were born into a relationship with another being. We are all the children of someone, and in that sense, all have a family. And even when those who've raised us pass away, the experience is in our history, it has shaped us, and can never be removed from our stories. In that sense, having had had the experience of being born into a family and being raised, we can never say we did not have a "family." Now, creating ones own family, meaning, trying, bearing, giving birth, and raising another being--is a different story.
Ultimately, I do not think that being child-free necessarily means that one will not have a family of their own. Family is what you make it. One can conceptualize family in many different ways that still makes one feel socially connected with others and this world. One can influence another so greatly that the other is changed--be it a child, adolescent, a friend, or older adult. There seems to be this idea that adults in society (and especially parents), should put efforts towards influencing the lives of children, since they are the ones still growing up, and will be the future, which I agree with, however, what about us helping each other out--adult to adult? It is as if such an influence is reserved for children and adolescents; something that stops once we are "adults." On the contrary, we can all help and inspire each other to grow! Thus, if helping each other grow is a way of thinking of family--we can all do it, with or without children!
ON "LEAVING A LEGACY"
The ideas I have just explained also correlate with the concept of "leaving a legacy" and "living on" after we pass. Having children simply because one wants to "leave a legacy" and "live on," appears to me as a way of limiting oneself and narrowing one's potential. That is not to say that this is not a valid reason, because if it is for someone, it simply is. But I would then ask them to think about what they mean by "legacy," because if legacy is being defined as an amount of influence left behind once one is gone, one's "legacy" will be limited to one's children. If that is what they want, perfect, but if one want to leave a greater mark on this world, one might want to think introspectively about how they will do it, beyond having kids.
But this is not to suggest that all child-free individuals, or anyone for that matter, want to leave a "legacy. Some are existentially and spiritually wise; content enough with the idea of dying and not leaving anything "behind," they simply want to live life, without a conscious care or effort to "leave a mark." It is a valid way to perceive life, since in the end, we will all die and life will never be as great as when we were actually alive to live it.
In summation, not having children simply means not being one of the directly responsible individuals who is raising a child into adulthood and beyond. Not having children does not mean not having a family. Not having children does not mean you cannot leave a "legacy," or that you have to!
But if you want some inspiration, watch this amazing man talk about the influence Oprah, who does not have or want children, has had on his life!