Good discussion. Here's my take on it:
Personhood occurs at either of 2 points, whichever comes first:
1) At birth, whenever that occurs
2) If still in utero, when the fetus reaches the age of natural viability. Which is when it could reasonably be expected to survive without intensive artificial life support if it were born. 24 weeks of gestational age is the lower limit.
Reasoning:
I would define a person as being a member of human society. To be a member of society, one has to be in society. Meaning one has to be born. Like being a member of a club requires going through some initiation process to be in the club. Birth is the initiation into the club of persons. But I will expand my definition to include a naturally viable fetus. This is one that could be reasonably expected to survive if it were born, with the same care given to any other newborn-- oral feeding, warmth, nurturing, etc. Natural viability is a more practically useful criterion for personhood than subjective things like cognitive ability or brain function. It's easily determined. There is good objective data on when it occurs. In the older pediatric literature, before the days of ventilators, total parenteral nutrition, lung surfactant, etc, a preemie born at 24 weeks had just over a 50% of survival. (Birth weight is also a factor in survivial, but that's harder to determine pre-natally.) Also, natural viability is much more biologically fixed, and will not be a continually moving target as neonatal life support technology advances.
Viability also dovetails nicely with the concept of balancing rights. I can understand the argument that an embryo might have a right to an undisturbed gestation. It is a gentically distinct individual. But it's physically attached to its mother, and makes a direct physiological demand on her heart, lungs, kidneys, and other organ systems. This is very different than a newborn, who makes no direct physiologic demand on the mother's body, and can thrive perfectly well under the care of anyone providing food, shelter, protection, etc. I believe the mother has a right to bodily autonomy, and must consent to her organ systems being directly used by another individual. I also believe such consent is ongoing, and the act of becoming pregnant does not imply automatic consent for a 9 month gestation. So as long as the fetus requires direct use of her organs, the mother's right to bodily autonomy supercedes any fetal rights. When the fetus no longer needs her bodily functions--which is when it's born, or when it's viable--then it becomes a person with its own rights.
I know all this is arbitrary, but any definition of personhood will be arbitrary. This is no more arbitrary than claiming a zygote is a person. But I also think it is fair, and reasonable, and sensibly balances the interests of a woman and a fetus.
