Thanks for this opportunity to (perhaps) bring some in the Liberty movement back to reason.
I personally believe most AnCaps and some Libertarians are simply so (rightfully) outraged at the abuses of people in government that they choose to violently reject the entire notion of government. It is terribly similar to many Atheists who reject the idea of God (however you want to define it) due to the crimes of man and organized religion. This is huge stumbling block that prevents us from moving forward, and from spreading the principles of Liberty. I believe there is a way forward, but it requires understanding the past.
Humans will always have something that functions as government, whether they want to call it that or not. Regardless of what you want to call it, something that performs the functions of government is a requirement for civil society. Again, call it private courts, private law, private security, private whatever, it still performs the same function.
The philosophical underpinnings of Libertarianism come from American Colonial Common Law. Simply put, ACCL was a way of resolving disputes of property (theft, fraud, harm or trespass), in a way that was restorative, just, and common to the people.
ACCL dictated that if there was no harm, there was no crime. Disputes that could not be settled privately were brought into the public by way of a claim against another man, a court was formed (venue was unimportant, sometimes it happened in the town square), a magistrate was chosen, a jury was convened, and the case was made.
The magistrate did not decide the case. They only made sure the rules of court agreed to prior were followed. The jury decided the case, and their decision was final. Judgments were determined according to what was common at the time, parties were either made whole, or in the case of false claims being levied, triple damages were the norm (bearing false witness was considered wrong).
Under ACCL everything was treated as property, even children and spouses. Within reason, everything was owned. Common spaces existed (streets, etc), but there was cooperative understanding and usage. If a common space or utility needed to be created or maintained, a town meeting was formed, and they hashed out what needed to be done. If crime started to get out of hand, they created a Sheriff, and paid him according to the custom of the time. Every subsequent community issue was dealt with by the community, participation was voluntary, and if you didn't agree to participate, you could leave.
It was a defacto Hoppean Covenant Community that evolved out of several centuries (perhaps millennia) of spontaneous organization since before even the signing of the Magna Carta. How our present "code world" system of law and governance came to be from that organic, cohesive societal organization, and how we might return - is another story for another day. But hopefully now you understand how and why things were organized, and hopefully could be organized again.
This is why I'm a Minarchist, and will never be an AnCap. I believe the nation needs a minimal government, kept to three things: Border protection, courts for contract dispute resolutions, and police to keep the peace/enforce contracts. Everything else needs to be left up to state and local governments to decide.
Assuming that removing government, as opposed to reducing centralized government and handing decisions over to local communities, is foolish; reasonable people rightly see it as such and reject it. Those interested in spreading Liberty will find themselves well served by promoting local control over central control, as self-determination is something everyone can get behind.
TL/DR Government: It doesn't matter what you call it, it only matters how you run it, and calling for the elimination of it (as opposed to clearly describing a better solution) just makes you sound like a hare-brained fanatic.