Your question seems to indicate that you feel the importance of the family has decreased in recent years in our time. Sociologically speaking, you could be right, as we have moved as a society away from the extended family towards the nuclear family, and some would argue that modern day society as driven us even further apart than this, stating the role of media and technology in isolating the members of even the nuclear family from each other.
However, even given this viewpoint, the state of the family today is very different from the role of the family in this brilliant dystopian novel. When Bernard and Lenina visit the Reservation, we have the perfect chance to see how life in this new world is structured by the so-called "barbaric" customs of those in the Reservation. Note what the Warden of the Reservation tells Lenina and Bernard about those living in it:
...about sixty thousand Indians and half-breeds... absolute savages... our inspectors occasionally visit... otherwise, no communication whatever with the civilised world... still preserve their repulsive habits and customs... marriage, if you know what that is, my dear young lady; families... no conditioning...
And so the list continues. We can see therefore that Huxley posits a future world in which advances in biological technology have dispensed for the need for women to "give birth" or for families at all. Such antiquated customs are seen as being "savage" and "barbaric." Therefore, fortunately, we still have a long way to go until the family is completely extinct.