(Dawkins is probably the world's most famous, or infamous, proponent of atheism, but a belief in atheism need not entail the pro-choice position on the ethics of abortion that Dawkins holds. Indeed, that position is contravened by science and reason accessible to people of any or no faith, independent of any religious teaching or texts.)
A clarification must be made regarding Dawkins' use of the term "human." It can be used in a biological sense to mean a living human organism—a member of the species Homo sapiens—and in that sense the fetus, from the beginning of his or her existence at conception, is a full-fledged human being, like you and me only at an earlier developmental stage, while the pig is not and never will be. But Dawkins uses "human" in a different sense to refer to certain characteristically-human qualities that he considers morally relevant with respect to how a being ought to be treated—qualities that may not be possessed by all human beings (those who have yet to acquire them, or who have lost them, are excluded from serious moral regard) and that may be possessed by some non-human animals (such as pigs).
Dawkins went on to further discuss abortion and clarify his position. He considers the ability to experience pain the decisive factor: Only beings who can feel pain deserve the sort of moral respect that would preclude killing them. Only when an unborn child is developed enough to feel pain is abortion (presumably) morally impermissible.
But this position does not seem defensible. Surely we may not kill people as long as we do so in a painless fashion. So it must be, as Dawkins puts it, the ability to feel pain that counts. But what about people who are under anesthesia or temporarily comatose? What about people with the condition called congenital insensitivity to pain? They cannot experience pain. Do they not still have a right to life? Imagine an intelligent alien race whose physiology is such that, though in every other way like us, they cannot feel pain or pleasure. Imagine a person whose brain has been surgically altered to prevent the experience of pain. Are these people not still people?
Even normal, adult human beings who can suffer pain have that ability in varying degrees. Does that mean that our moral worth, our right not to be killed, is also a matter of degree? Are some people more valuable than others? Philosopher Christopher Kaczor writes:
The kung fu master can put his arms around a burning cauldron, endure the searing of flesh, and carry the weighty object. The proverbial princess cannot stand the pea under her multiple mattresses. Many men cannot bear the least discomfort, and many women endure childbirth without anesthetic. Certain injuries and diseases greatly hinder the human capacity for pain, as do drugs of various kinds, as do differences in degrees of concentration and experience. ... Our experiences of pains and pleasures are conditioned by our prior experiences, beliefs, and habits. Since no two human persons have the same experiences, beliefs, and habits, no two human persons have equal capacities for pleasure and pain, and therefore human persons do not have equal rights [if rights depends on the ability to feel pain, which Kaczor rejects].This is not to say that pain and suffering are morally irrelevant—clearly they matter a great deal. But it is just as clear that the ability to experience pain is not a necessary criterion for having a right to life or for deserving the kind of moral respect that precludes killing for socio-economic reasons. Nor can the ability to experience pain serve as the basis for equal dignity and rights.
Dawkins will have to rethink his position. (In the meantime, he can at least support current legislation in the United States to stop the dismemberment and killing of unborn children developed enough to feel pain.)