Sorry, but you are not addressing my point: it is not enough just to declare it is a "false dichotomy" - you have to show precisely why. Here is my point again:
To justify your disagreement, you must show precisely where my reasoning went wrong.
This is a very mechanical and sociopathic view on humans. Probably you've read too much Hoppe or Ayn Rand. Humans are not machines. They also have the capability to share things without involvement of a state.
I will respond you despite your offensive tone.
My point is precisely the opposite: neither the division of labor nor the resulting need for exchanging the products of labor depend on the state. It is you that are holding the opposite view, despite yourself calling it "sociopathic."
That is why it is a false dichotomy, very clearly.
It is not even clear precisely
what you are calling a "false dichotomy."
Or do you use currency in your own family to trade tit-for-tat?
My uncle bought my old monitor, does that qualify?
Similarly, ancient societies consisted of tribes, i.e. extended families. That's why the step to minted coinage is not as straightforward as you believe it to be.
Primitive forms of money are salt, grains, etc, not coins. You are ignoring thousands of years of economic development.
Still, they also had "division of labor" to some degree nevertheless.
Money does not originate directly from the division of labor: it originates from the problems posed by direct commodity exchange, which in turn originates from the division of labor.
For larger tribes they were some kind of reputation systems in place, if you read anthropologists like Professor (and anarchist)
David Graeber, who dispels many myths like Adam Smith's thought experiment (nothing else it was) about the origin of money from barter.
Did Mr. Graeber manage to generalize exchange without using money?
At larger scale, things surely get more complex, but I mentioned that myself. Even then there are other approaches without requiring a state.
Again, my point is that
neither the division of labor
nor the resulting exchange of labor products, whether monetary or not, depend on the state. It is you that are holding the opposite view.
Again, you should watch the linked documentaries to broaden your horizon, just a little. You have this reductionist view that is too typical for US Libertarians, it already has become a cliché.
If you refer to the idea that money depends on the state - which is usually not a libertarian view - then again: I hold precisely the opposite view (namely, that money does
not depend on the state).