Let's assume that claim to be true. If you own yourself, then you can sell yourself. After all, the ability to transfer ownership is said to be a key pragmatic test of ownership. This means slavery is a logical potential pragmatic consequence of anarcho-capitalist principles, if it can be said to have any principles at all beyond the principle of control.
Now, that's not necessarily a problem. After all, if I am properly considered property, then I can be bought and sold, and if I own myself, then I consider myself properly property, and must necessarily agree that I can be bought and sold. If I cannot be bought and sold, then I do not own myself.
Which means that the black slave trade was legitimate by anarcho-capitalist standards, as is buying and selling body parts from the living bodies. And we may add other unsavory examples to this, such as enforced sexual access to the slaves - after all, you own them, just as you own your animals and your house. And like animals, you own the products of their bodies, too - which means you own their children, and so on.
But wait! The slaves were kidnapped! They didn't voluntarily submit to slavery! And so also with much of the organ harvesting! And so on.
Why should I care about that? Under anarcho-capitalism, all I care about with respect to buying stuff is I freely paid what the seller was charging, therefore ownership transferred to me. I haven't got any real way to check whether it's stolen property I'm buying, do I? And who says I should have to check whether a seller freely bought or produced his wares? And the claim that the product I purchased was gotten by force or fraud sounds exactly like something someone who had sellers' remorse would say. It would be odd if sellers' remorse negated economic transactions after the fact, wouldn't it?
So... say hello to human (parts) trafficking, thanks to anarcho-capitalism. For those who believe life cannot be reduced to monetary valuation, this will seem to be problematic, indeed.
Oh, there are other problems. Suppose we all lived in a Libertarian utopia, and private security firms supplied protection services to signatories. Of course, unborn fetuses are not going to be able to sign an agreement with, nor pay, a security firm. Surely potential parents might insure fetuses, and insurers might employ security firms to acquire recompensation from those who might harm an insured fetus. But suppose the potential parents have a Swiftian taste for human flesh. They refuse coverage, stroll out onto their lawn, where Mom squats and squirts out a live, lusty, screaming newborn son, who is promptly strangled with his umbilical cord by Dad, dusted with seasoning, roasted on their barbeque pit, and consumed in full view of the neighbors. Well, that's ok by anarcho-capitalist standards. After all, when you don't, or can't, pay for protection, you are prey. Who will defend you? Who can? After all, only signatories are covered, which means if a signatory is murdering and butchering non-signatories, no other signatory can defend the non-signatories without becoming liable for assault against the signatory.
But suppose this is too easy. Maybe a security firm will initially defend non-signatories for free in a nominally protected zone... but then, they gotta get theirs, right? Can't make money by giving charity to bums or else everyone will try for a free ride. So it'll probably work like it did in ye olden days, where if you are on a protected territory, and services are provided, you may be compelled to pay for them - slavery, in a word. Gotta get paid, and babies can't pay, but might be able to be sold - how can you have property rights you can't assert? Bums might could work.
The alternative strategy to ensure getting paid seems to be exaction of tribute, or taxation... which implies a State, as defined per the anarcho-capitalists: an organization holding monopoly rights on the application of violence within a territory.
And abortion "rights" would be guaranteed in such a mercenary "voluntaryist" anarcho-capitalist society. Remember: you own yourself, and if someone touches your shit, including yourself, you get to kill them: that is the meaning of property. It doesn't matter that the fetus only came into existence due to your activities; after all, you can hardly be blamed for someone else trespassing on your rightfully owned stuff, can you? Isn't that like victim blaming or something? Just because the crime of trespassing can't exist without claims of ownership doesn't make owners as a class responsible for the existence of trespassers as a class, does it? While I don't consider those questions rhetorical, those sold on the concept of private property will. The gist is this: in a system predicated upon self-ownership, in which bodies are propertly considered property, the fetus is trespassing, no matter their intent or lack thereof, no matter how they got there. Property rights are absolute, and above life, in such a system.
Because there is only one human right in this system. Just ask Rothbard.