Anarcho-Capitalism

My argument will have two parts. First, a justification of capitalism, and then a de-construction of the concept of 'government'. These two arguments however will overlap and I will draw on some premises from my 'Capitalism argument' to apply to my 'Government argument'.Argumentation- CapitalismCapitalism was not officially defined so I will attempt to do it here. This definition may be brought up as a point of contention if my opponent sees problems with it. So I will define a capitalist economy as one based on the concept of private property and voluntary exchange between individuals. So to justify a system of capitalism, private property and voluntary exchange must be justified.Premise 1: The homesteading principle implies justification of private property rights.While the homesteading principle does not mention the idea of 'private' property specifically, it does imply that individuals are able to acquire property on their own, without regards to a government or outside body, so long as the property in question is unowned. Premise 2: Ownership also implies the ability to use said property in any non-aggressive or sufficiently justified means.This premise is self-evidence. It is simply definitional. If I 'own' something. I can do whatever I want with it and be justified in doing so, so long as I do not infringe on another's property rights.Premise 3: Voluntary exchange is a means of using property that does not necessarily infringe on another's property rights.While there could be cases of voluntary exchange infringing on property rights(two people 'voluntarily' trading another person away), the concept of voluntary exchange does not necessarily infringe on property rights. If both parties are justified in their acquisition of said property, the concept of ownership allows them to exchange these properties, so long as they both agree to the trade.Conclusion 1: Capitalism(private property and voluntary exchange) is a justified economic system.- From P1-P3Argumentation- AnarchismPremise 1: Any government(minarchist, socialist, fascist) is necessarily a monopolist on arbitration and law(and in some cases morality, industry or property).- Definitional premisePremise 2: Monopolies are unjustified.My reasoning for this premise draws largely on my capitalism argument. Given, the homesteading principle(and it's necessary implications of private ownership and justification of voluntary exchange), monopolies cannot be justified. For there to be a monopoly on something, the monopolist must force competitors out of the market(in the government's case, it uses "law"). But to do this, one would need to infringe on another's property rights. To not allow someone to voluntary exchange goods or services(in this case arbitration), is a clear violation of their ability to exchange said services and thus an infringement on their property rights. To use an example, let us take toilet paper. Let's say that there is a company who manufacturers toilet paper. And they believe that their toilet paper is best, so they force all other competitors(even one's that would possibly supply better toilet paper) out of the market. Would this not be a clear infringement on property rights and thus be unjustified? This situation is analogous to a government's monopoly on arbitration and law. If a government really does provide better arbitration or law over legal disputes, it should be decided via a free market where consumers can decide for themselves who provides the better service.Conclusion 1: Government is not justified.- From P1 and P2This is the logical conclusion of P1 and P2. G is M. M is not justified. Therefore G is not justified.I will expound on the specific premises or conclusions that my opponent finds fault with in later rounds. But for now I will toss the debate back to my opponent.