Let's begin with the foetus as not being a nephesh.
Let's begin here:
“While the Talmud does discuss the time of ensoulment - is it when the child is conceived, or at the first trimester, at birth, or, as one opinion has it, when the child first answers ‘Amen’? - it dismisses the question as both unanswerable and irrelevant to the abortion question.
Abortion then is neither murder nor worse than murder, nor an option when the alternative is death to the mother. Since the mother is not allowed to choose suicide, abortion in that extreme case becomes necessary. This is the sense of the fundamental Talmudic passage on the subject.”
- David Feldman, “Jewish Views on Abortion” in Steven Bayme, Gladys Rosen (eds.), The Jewish Family and Jewish Community, (1994), p. 239
Further: Feldman continues:
To begin to make his case, Feldman points out that there is no Commandment reading "Thou shalt not kill": rather, the Commandment reads "Thou shalt not murder." In Judaism (and elsewhere, of course) killing in self-defense is allowed. There are a number of categories of allowable killing in self-defense - including the category "of rodef, the aggressor, who may be killed if that is the only way to stop his pursuit or aggression of a third party." The Talmud considers treating the fetus as a rodef - specifically, "an aggressor against its mother, and making that the reason why abortion to save the mother's life is permitted."
But the Talmud proceeds to reject that reasoning on the obvious grounds that the fetus is not yet of responsible age to deliberately forfeit its protection against being murdered [i.e., by consciously choosing to act as an aggressor, and thereby loosing its protection against killing]. The only valid grounds for permitting even therapeutic abortion is that murder is not involved because the fetus is not yet a human person [ftn. 1: Sanhedrin 72b: David Feldman Birth Control in Jewish Law (New York: New York University Press, 1968), chaps. 14 and 15.] Killing is admittedly involved, but not murder. Killing is the taking of life of, say, an animal or a chicken, or of a human who forfeits his protection by an act of aggression. (81)
This brings us to the central point: the crucial distinction between killing and murder further depends on the definition of the status of the life taken - a definition which Feldman observes is metaphysical and religious, rather than scientific: <snip>
The abortion question in talmudic law revolves around the legal status of the embryo. For this the Talmud has a phrase, ubbar yerekh immo, which phrase is a counterpart of the Latin pars viscerum matris. That is, the fetus is deemed "a part of its mother," rather than an independent entity. This designation says nothing about the morality of abortion; rather, it defines ownership, for example, in the case of an embryo found in a purchased animal. As intrinsic to its mother's body, it belongs to the buyer. In the religious conversion of a pregnant woman, her unborn child is automatically included and requires no further ceremony. Nor does it have power of acquisition; gifts made on its behalf are not binding. These and similar points mean only that the fetus has no "juridical personality," but say nothing about the right of abortion. This turns rather on whether feticide is or is not homicide. (81-82)
Even given the designation of the embryo / fetus as intrinsic to the mother's body and thereby lacking, we might say, personhood - is feticide, the killing of at least a potential human being the same as homicide? The biblical books of Exodus and Leviticus (part of the Torah - teaching, path, law - in Judaism, and canonical "Old Testament" books for Christians), as understood through the Talmud and Rashi (one of the most important Rabbinic authorities), argue that the answer to this question is, "No."
The law of homicide in the Torah, in one of its formulations, reads: "Makkeh ish..." "He who smites a man..." (Ex. 21:12). Does this include any many, say a day-old child? Yes, says the Talmud, citing another text: "...ki yakkeh kol nefesh adam" "If one smite any nefesh adam" (Lev. 24:17) - literally, any human person. (Whereas we may not be sure that the newborn babe has completed its term and is a bar kayyama, fully viable, until thirty days after birth, he is fully human from the moment of birth. If he dies before his thirtieth day, no funeral or shivah rites are applicable either. But active destruction of a born child of even doubtful viability is here definitely forbidden.) The "any" (kol) is understood to include the day-old child, but the "nefesh adam" is taken to exclude the fetus in the womb. The fetus in the womb, says Rashi, classic commentator on the Bible and Talmud, is lav nefish hu, not a person, until he comes into the world. Feticide, then, does not constitute homicide, and the basis for denying it capital-crime status in Jewish law - even for those rabbis who may have wanted to rule otherwise - is scriptural. Alongside the above text is another one in Exodus that reads: "If men strive, and wound a pregnant woman so that her fruit be expelled, but no harm befall [her], then shall he be fined as her husband shall assess...But if harm befall [her], then shalt thou give life for life" (21:22). The Talmud makes this verse's teaching explicit: Only monetary compensation is exacted of him who causes a woman to miscarry. Note also that though the abortion spoken of here is accidental, it contrasts with the homicide (of the mother) which is also accidental. Even unintentional homicide cannot be expiated by a monetary fine. (82)