Logically, personhood begins with the fertilized egg. The idea that the conceptus (= fertilized egg) is not a "person" but becomes a person somewhere along the way is rejected by atheists and theists alike. I call this the "sudden personhood" argument; viz., that the conceptus is not a person but eventually becomes a person.
An atheist has reason to reject the sudden personhood argument because atheism implies that human life has no "soul." Therefore, there is nothing special about persons. Persons, on atheism, are simply animals. Human animal life begins with the fertilized egg, and nothing "special" (i.e., "becomes a 'person')happens on life's journey.
Christian theists believe personhood is defined by having a soul. The human soul is not somehow inserted into a fetus along the developmental way. If so, how could this be determined?
A conceptus is as much a person as you or I. Do you have pictures of yourself from 10 years ago? That was you. Do you have pictures of yourself as a baby? That was you. Do you have intrauteral ultrasound pictures of yourself? That was you. If a picture could have been taken of you as a conceptus - that also was you. "You" were once a fertilzed egg. Had someone aborted you, "you" would not be here to tell about it.
As a conceptus you were helpless to protect yourself. You were extremely limited in your abilities. But the potential was there to develop greater abilities. I believe it is most rational to hold that the conceptus is fully a person. Then, we do best to hold to a developmental view of personhood in the sense that persons grow and change while being, at root, the same person.
For deeper study read Francis Beckwith's book Politically Correct Death.