Anarchocapitalists define anarchy as meaning without rulers. The private property rights of anarchocapitalism are derived from the principle that you own yourself and therefore can use your time and labor to create for yourself or trade it resulting in you owning the benefits of your labor. Without rulers also plays into the ancap catch phrase the non-aggression principle, by which we mean we believe it is wrong to initiate force on another, which renders governments illegitimate. Instead, ancaps wish to use voluntary market systems to provide everything that we need which is basically how the world already works except there is a leech known as government that sucks off of it and regulates it for its own benefit.

Also, why can contract and credit enforcement not be done without a state? If we make an agreement that you will send me fresh apples and they arrive late and aren't good to eat wouldn't you likely provide me with a refund to ensure repeat business and to provide assurance to other customers that they are guaranteed a good product for their money or they get it back? Just sounds like good business. Say I am renting you my house, I would have you sign a contract that if you don't pay you don't stay. If you don't leave I will have you removed. If you don't pay do I need a government to remove you? Right now private companies do that, police may escort them, but I don't see why someone else without a badge and funny costume couldn't do the same thing. In Detroit there is a great private security company called Threat Management Center that escorts people to court for free and patrols areas in Detroit because local businesses pay them to when the police failed them. So this is completely possible.

As far as credit, you can loan your cryptocurrencies to traders right now on a number of exchanges. Banks can't loan without government? It would definitely not be as easy without being able to loan money into existence but they could do it. They did it in the past and we do it now with crypto so I am not seeing how that argument holds. There's also non banking loaners all over the place but I feel like I am just beating a dead horse here.

Nothing you have said shows that you have any real understanding of what ancaps think or provide any contradictions in anarchocapitalist logic. You defined anarchism in an anarchosocialist style while ignoring the ancap definition and said that is why it has contradictions. The rest was just your opinion of implementation and sounds nothing like what an ancap would describe.