Regarding the notion of "self-ownership"
I do not own myself. I am myself. The ownership relation (as in, "I own X") is between an agent and something external to that agent. The agent cannot own himself, because he is himself. He is not external to himself and thus cannot claim that he "owns" himself. The use of the verb "own" in such a context is incoherent, because such a use contradicts the meaning of word "own" when utilized as a verb.
Furthermore, it also cannot be coherently asserted that "I own my body". Because there is no consistently meaningful conceptual delineation between oneself and one's body. Even if there were a meaningful conceptual delineation between oneself and one's body, there is no explanation for how one comes to "own" oneself that can be used to justify private property rights.
Addressing objections to this critique of the concept of "self-ownership"
The best objection I have come across is that "self-ownership" is a misnomer and that actually what the concept is, is the fundamental notion that one owns his/her body. While this is certainly an improvement from the notion of "self-ownership" (in that it is not immediately self-refuting), it still is irreconcilable with AnCap defense of Private Property Rights. There is simply zero logical consistency between the defense of bodily ownership and the defense of private property ownership.
When pushed, AnCaps will say that the basis by which one owns his/her body is that you - the individual in question - are the person with the most direct control over your bodily functions. You control the movements of your hands, legs, etc... more so than anyone else can be said to. Therefore, you own your body. But the problem is that if the extent to which one directly controls something more so than others is the basis upon which legitimate ownership claims rest, then workers own the MoP rather than Capitalists.
At this point in the critique, is when AnCaps split into two kinds of responses:
(A) One kind of response essentially admits that the basis for ownership of one's body is fundamentally different from the basis for ownership of MoP. They say that the basis of ownership of one's body is based on classical liberal Natural Rights.
(B) The other kind of response says that the basis for ownership of one's body is based on the fact that you homestead your own body. But this is simply incorrect. Based on homesteading principles applied consistently, your parents would actually own your body.
So only response (A) is left unrefuted by AnCapism's own rules and principles. I'll stop here, because there are specific and well-known criticisms of classical liberal notions of Natural Rights that many of us are familiar with. So even (A) is refutable with those arguments.