Murray N. Rothbard from The Ethics of Liberty:

The proper groundwork for analysis of abortion is in every man’s absolute right of self-ownership. This implies immediately that every woman has the absolute right to her own body, that she has absolute dominion over her body and everything within it. This includes the fetus. Most fetuses are in the mother’s womb because the mother consents to this situation, but the fetus is there by the mother’s freely-granted consent. But should the mother decide that she does not want the fetus there any longer, then the fetus becomes a parasitic “invader” of her person, and the mother has the perfect right to expel this invader from her domain. Abortion should be looked upon, not as “murder” of a living person, but as the expulsion of an unwanted invader from the mother’s body. Any laws restricting or prohibiting abortion are therefore invasions of the rights of mothers.

     It has been objected that since the mother originally consented to the conception, the mother has therefore “contracted” its status with the fetus, and may not “violate” that “contract” by having an abortion. There are many problems with this doctrine, however. In the first place, as we shall see further below, a mere promise is not an enforceable contract: contracts are only properly enforceable if their violation involves implicit theft, and clearly no such consideration can apply here. Secondly, there is obviously no “contract” here, since the fetus (fertilized ovum?) can hardly be considered a voluntarily and consciously contracting entity. And thirdly as we have seen above, a crucial point in libertarian theory is the inalienability of the will, and therefore the impermissibility of enforcing voluntary slave contracts. Even if this had been a “contract,” then, it could not be enforced because a mother’s will is inalienable, and she cannot legitimately be enslaved into carrying and having a baby against her will.

     Another argument of the anti-abortionists is that the fetus is a living human being, and is therefore entitled to all of the rights of human beings. Very good; let us concede, for purposes of the discussion, that fetuses are human beings—or, more broadly, potential human beings—and are therefore entitled to full human rights. But what humans, we may ask, have the right to be coercive parasites within the body of an unwilling human host? Clearly no born humans have such a right, and therefore, a fortiori, the fetus can have no such right either.