You don't need a monopoly on self-defense. You can easily imagine people organizing and financing their own defense through many private companies, organizations, and of course by themselves.
If you were right, we would already have a world government. Yet we still have many states coexisting, both big and small. Now let's imagine that one day, enough people with similar views on freedom and property gather in one place (it could be land bought piece by piece incrementally over time, international waters, space, etc.) and decide to finance their own defense. That would quickly become the most powerful defense system per capita, for sure.
You are conditioned to see the world through the prism of "the State" because that's all we've known. But social structures evolve with time and context, which is mostly driven by technology. We went from hunter-gatherer tribes to what we have today, so...
But there is no such thing as a State in an ancap society. There are only individuals and decentralized organizations that are intangible and difficult to capture. What exactly do you capture as an attacker if you can't seize the centralized entity that runs everything? Is it even worth going to war, and for what?
The necessary evil you call the "State" is, in this view, a network of individuals bound by contracts, incentives, and values.
