The personhood argument is strong but it seems to go too far. It is intended to defend abortion only, but it can also lower our view of newborn babies. A baby has no understanding of self any more than a fetus. 
     Peter Singer says, “Human babies are not born self-aware, or capable of grasping that they exist over time.” With this understanding, he concludes, “the life of a newborn is of less value than the life of a pig, a dog, or a chimpanzee.” He says, “When we kill a newborn, there is no person whose life has begun. When I think of myself as the person I am now, I realize that I did not come into existence until sometime after my birth.”
     Pro-choicers typically use the personhood rationale to support abortion-on-demand, but such reasoning could also support infanticide, because a difference in location (outside the womb) cannot change the perceived worth of a being.  Peter Singer proposes a solution to this problem; he concludes that birth can change the status of the infant but not because the infant has attained worth in itself. The infant’s status can change because of value that others might attribute to it. The woman no longer has the same claim on the child’s life that she had before, because other people can offer to take the infant at this point. Still, some societies leave infanticide as an option for families that choose not to take care of the child, and Singer has no problem with that. The pro-choice view shies away from the idea that a child has value independent of the views of the people around it.
* Practical Ethics, 1st ed. 1979 pg. 122-123 Cambridge University Press. Last quote: H. Kuhnse and Peter Singer, Should the Baby Live? Pg. 133 (New York: Oxford University Press, 1985)