I can see a couple ways to add definition to why and why not, and what it would mean.
There is some dispute about reproductive division of labour, but there is a strong case to be made that humans are eusocial - they share some of the qualities of hive organisms. I feel the near universal existence of traditions of religious celibacy is the strongest argument for this. It may no longer be strictly true, but it was in the situation homo sapiens sapiens evolved in, especially as made it through the long bottle-neck around 70,000 years ago, where it seems our lineage gained a decisive advantage over other homonids, and spread dramatically further than any previous wave out of Africa. From Dunbar's number, we can deduce that humans have a strong preference for a group size of around 150, confirmed by the Domesday Book, and archeology (cities are evolutionarily very recent, & co-arose with animal domestication & writing, and can be considered as organisms in their own right). I would suggest that like bees, historically a succesful human colony would reach a certain critical mass, and spin-out a new 'swarm', in past times. With humans the increase in population and preperation to succeed in new wilds and/or against other troops of humans, would often involve a new edge in technology (eg Clovis people getting to North America), driving the spread of progressive sophistication. Tribe members would be quite closely related, helping stabilise traits, but be large enough to reduce the risks of inbreeding. Clan, tribe, village, and extended family, are all approximate synonyms. It would seem the minimum size group to be self-sufficient, and stable, with a set of different skills & traits that balance out & form a stronger whole. Including, the need for collective decision-making, & being a kind of proto-state. Dunbar's number links to how many faces & characters we can remember, and it makes sense that decision making bodies like the Houses of Parliament & Congress are around this size (NB typical attendence, rather than potential attendence). It's like a village of village-representatives makes a council, & a council of council-representatives makes a government. The Pareto distribution of human connectivity provides interesting insights to this.
The next strand I would look at is Peter Singer's 'expanding circle of moral concern', which I would say gives the best account of what we call moral progress. In this view we began with a concern for our own offspring, and this got 'hijacked' to apply to a kin selection group (there's great comparative evolutionary arguments for this happening many times). Humans had a strong pressure to develop uniquely many mirror neurons, because of evolving to access bones, shellfish, & coconuts which no or few other animals could, and the need to mimic detailed actions of others to do this (supported by creche-rearing infants). Sophisticated tool use does not always correlate with language, but tool use & this high degree of intersubjectivity (from mirror neurons) does seem to, as in parrots & dolphins, ie quick learning from mimicking others, means complex language. From multi-level selection theory, the reboot of failed group selection theory, we see offspring-preference & kin selection are still primary, the unit of selection is still the individual's genes. But, inter-group cooperation that provides additional benefits without harming these, has clearly gained a strong selection pressure, and we have come to consider expanding our circle of concern from immediate family, to kin, to all humans, to non-humans, steps in moral progress, eg ending slavery, declaring universal human rights, establishing animal rights. I would argue morality & ethics 'hijacked' shame & disgust, and we developed social reinforcement to direct these to support positive group-directed behaviour, and we call this ethics & morality (look at the Greek tradition of the Furies, unleashed by paricide, incest etc, to see the transition from more instinctive, to more reasoned & legal constraint).
So, after that bit of lengthy beating-about-the-bush, I would say yes the state can be thought of as a family - but better as a tribe or tribe-of-tribes. But, moral progress is towards thinking of the human family, towards concern for all sentient beings. And any state which seeks to constrict or prevent an individuals reproduction, violates a kind of evolutionary social contract - and the reason that's a problem is the same that kaiboshed group selection: if a strata get to control the reproduction of non-kin, you get a free-rider problem, which makes the situation unstable. Those controlled in this way will always see the controllers as oppressive, and those controlling will have a distancing from the production of resources because of the decoupling from the group that create them (if there is no social mobility or mutual gene-flow), which will impair their fitness. This accounts for a great deal of human history, and the stability of democratic socialism. I would argue it points to sources of instability in the USA & China, around lack of social mobility even over generations (India is less economically unequal than the USA!), and the pressure resulting from that to generate an out of touch elite incapable of making decisions for the benefit of the whole population (I'm not saying that currently does or has to happen, there are checks-and-balances, but it's a constant risk).
As an aside, I'd note the derivation of company, and companions, from 'with bread', those we break bread with. State and family are in some sense imposed, or non-optional, but there is another strand here. Modern states greatly benefit from pressure-groups, they are pretty essential, and I would say they follow this rather than a 'family' model, usually anyway.