There are a lot of good economic arguments in favor of libertarianism and anarchism. For example, often you'll hear that free market capitalism works better than state intervention, that private institutions are more efficient than government bureaucracy, that the state can't do price calculation, and so on and so forth.
While these arguments are all quite strong and the working of free markets has been proven many times, they often don't win you debates. You'll often get responses like: "You only care about your stupid economy," or "But what about the poor?" or "But everyone has the right to X, Y and Z."
In my opinion, economic arguments are the least powerful to advocate for libertarianism. Firstly, because many people don't have deep knowledge about economics. Secondly, because the people you argue with care more about other things. Thirdly, because it instantly builds a barrier between you and your conversation partner and you'll get responses like the ones I just mentioned.
Moreover, when libertarians advocate for free market enterprise, they don't really talk about economics, but rather about a concept called catallactics. This is because libertarianism advocates for voluntary exchange, regardless of what those exchanges are, rather than the social engineering that economists tend to advocate for. As James Corbett of the @corbettreport points out in one of his international forecasters:This also explains why economists are doomed to fail in their attempts to construct the perfect set of policies for directing the national economy. There is no such thing as a unitary plan to balance out the needs of any group of humans, let alone entire nations. Worse yet for the would-be managers of human activity, even the idea of a "best fit" plan or some utilitarian "greater good" policy package for the direction of resource allocation is a pipe dream. Human values are incommensurable, to say nothing of material w...