Rajiv Shah has written an entry about the nonsense of “self-ownership” and all its standard problems: it is self-referential, it assumes a specific version of property, and the bizarre logic of “if I don’t own myself, then others do.” A great read.
As Ed Feser (2005) argued, if Cartesian dualism is true (and it is not incoherent for the self to own itself) then the body is a form of external property. This means that provisios relating to its use such as (on one interpretation) Nozick’s Lockean provisio and Eric Mack’s Self Ownership provisio would also apply to it. This means that there will be constraints on how one can use one’s body. This is a conclusion inconsistent with the traditional implications of SO.
In his article Feser goes through various conceptions of personal identity and considers their implications for SO. He concludes that none of them yield the standard Rothbardian view.
To conclude, there are two possibilities. (1) (If one rejects a dualist conception of the self) SO is incoherent (2) (Assuming the self referential aspect of SO does not make it incoherent) not all conceptions of the self will yield libertarian conclusions; indeed it might be that no conception of the self yields those conclusions. Either way, asserting SO is not enough a libertarian would also have to defend a particular conception of the self.