According to the Founding Fathers, a fetus is not an American person. The United States Constitution clearly indicates that human life begins at birth, not at conception.
There are some obvious signs that the Framers did not suppose that the embryo was already a person. When they put the age of eligibility for the presidency at 35, they clearly weren’t calculating from the moment of conception. Nor were they thinking one should be at least 17 years and 3 months old when they guaranteed the right to vote at age 18.
More telling is what one might call “the problem of the foreign fetus.” If a fetus is already a person, then a foreign individual could legitimately be elected president of the United States. Consider the case of an immigrant couple—German, Russian, Kenyan, or whatever—who have completed the residency requirements for U.S. citizenship, conceived a child, and then become naturalized citizens before its birth. Now born of American citizens, the child is eligible to become president even though, as an embryo, it was a foreigner. Would the people who believe that human life begins at conception really want a Kenyan person to become president of the United States?
Then there is the proverbial problem of “it’s a wise child that knows its own (biological) father.” This becomes a constitutional predicament in the case of a person who is presumably eligible for the presidency because her father is a citizen, though her mother is not. What is to guarantee that biological father, and therefore the fetus, was an American citizen? Most modern societies resolve such issues by adopting the principle of the Napoleonic Code that defines the father of the child as the husband of the mother. On the premise that the fetus is a person, however, we would have to get into genetic investigations. A DNA test might indeed identify a father who was citizen; but then again, it could be anyone—nor could you tell whether he was a citizen from the DNA.
In short, the presumption that a fetus is a human person is unconstitutional.
The more general principle is this: in all known human societies, one's identity as a person is established by membership in the society, which necessarily depends on the observable circumstances of birth rather than the occult moment of conception. At birth one is attributed the parentage, name, local affiliations, kinship relations, citizenship, and other social specifications that define a human existence. All this, moreover, is publicly certified by rituals, such as christening, that typically confer legitimacy on the newborn by society, as backed by divinity. One is a person by culture, not by nature.