To start with, atomism here refers to making parts primary over wholes. There are two forms of atomism relevant to the abortion debate: social and medical. Social atomism holds the individuals in society as essentially independent. Medical atomism treats the parts of a person as essentially separable, and so as individually treatable. The former tends to view each person as prima facie on their own. The latter tends to do the same with various parts of a person. Parts of a person can be their eyes, their stomach, their heart, etc., or their blood pressure, their digestion, etc. Both are "parts" as opposed to a holistic view which assumes that the problem appearing in one part of the body may lie in a prima facie unrelated part.
Now, then, a fetus or unborn child tends to be regarded, by both sides of the debate, as separable from the mother in both of these ways. Certainly, they are distinct persons, but one is dependent on the other and they are organically and naturally linked to each other. The pregnancy produces changes in the mother's neurochemistry, and the child is affected by various conditions the mother may be put in, whether sickness, stress, or consuming various things. These are largely ignored by a medically atomistic view, particularly insofar as these relations might be seen to affect the morality of certain choices. Medical atomism tends to assume that, while drug A may have some bad affects, adding drug B can counter that, and so one just has to find the right combination of drugs. Thus, natural processes are seen as overcomeable, and thus as only relevant insofar as they are cheaper or more convenient ways of dealing with health conditions. This moves against the idea of natural law, which, in many forms, assumes we can, to some degree, read off morality from how things are put together.
Likewise, the unborn child or fetus is almost always regarded as separable from the mother socially. This is done when they are treated as equal bearers of rights which may come into conflict, and nothing more. The location of the child within the mother and essentially dependent on the mother for life and sustenance are largely ignored.
In our society, very little is made of rights and duties of parents to children and vice-versa, particularly after the child moves out. In a sense, the abortion debate raises the question of whether the rights and duties begin before a certain period.
Where does a right to provide for one's offspring originate from? If that question can be answered, then, it seems reasonable to think, we will be able to find when it originates. If it originates biologically, then, depending on how that is fleshed out, the duty will begin when those biological conditions are met. If the duty arises from an implicit promise made by parents in intentionally conceiving a child, then unintentionally produced fetuses will lack a right to sustenance in the womb--or out of it, for that matter, depending on whether failure to abort is then considered another way of implicitly promising continued care. There may be other ways of deriving the right, and the former needs more fleshing out. I actually suspect that most pro-life supporters are relatively speciesist, whether for theological or naive reasons, neither of which are helpful (even if right) in secular debates.
I am inclined to think that the latter, implicit promise, model is implicitly held by those who want abortion to be legal. Notably, it fits a social contract theory, which theories often strike me as socially atomistic.
One problem which faces the ongoing debate about this issue is a lack of depth. That is, while a pro-life advocate can provide an ethical theory of why they are right and pro-choice advocates are not, the same applies the other way around. Neither has been able to upset the others' meta-ethical positions. In order to do so, the pro-choice advocate needs to provide good reason for the pro-life advocate to give up her biologically rooted ethics (which, actually, should have been pretty easy, thus my suspicion of speciesism). The pro-life advocate, on the other hand, needs to dislodge a social contract point of view which is relatively well linked to notions of autonomy and democracy.
Returning to my points about atomism earlier, then, I want to persue the question of how a shift to a more holistic standpoint might affect our meta-ethical positions, and thus our views on abortion.
First, a holistic standpoint must recognize interdependencies between parts, and the way the parts form the whole. The fact that abortion is an induced miscarriage, and the trial which miscarriage is seen to be by virtue of biological processes which we do not understand well, leads us to view abortion as trialsome, whether or not we come to see it as justifiable in any particular case. This is medical holism, and can be continued in basically the direction of normal natural law arguments for a pro-life position. It will also be noted, however, how the pregnancy affects the mother besides eventually bearing a child, that is, particularly, how it may disrupt life plans. Within this perspective, I think, we would want children to be raised by their biological parents--as an ideal, not a requirement. Thus, giving up a child for adoption would be seen as a lesser of two evils. This shifts us towards a social holism. This does assume a humble holism which is thus wary of going outside the biological setup. Such could be justified either by reference to God's goodness in creation, or to epistemic humility.
Second, holism would force us to ask about what affects the laws might have beyond what they say simpliciter. Thus, for instance, does legalizing abortion tend to present children as a burden? Does not doing so present women as unneeded outside the home? Do the tendencies encouraged by these laws promote attitudes and behaviors we approve of or not? Do they encourage situations which are conducive to things we approve of? Thus, legal holism asks: What do these laws teach? What kinds of laws fit into the present structure of laws? Is that good?
Finally, we might also ask whether those presently making the laws concerning abortion are the right ones to be doing it, along similar lines: Should this body have this power? That is, independently of the decisions being made, should the power being exercised by this body belong to this body, or is this body taking power which rightfully should belong to another? Of course, this gets us a bit afield, asking what the purpose of various parts of government are, as well as the purpose of government as a whole (and how the parts interact, etc.).
On the other hand, we should try to show what the problem with social contract theory and its atomism is. Briefly, I would suggest that social contract theory tends toward political and ethical voluntarism, thus removing any solid root from which to argue ethically, and atomism tends to produce division in social bodies, as well as to ignore feedback loops, and unintended consequences. It thus oversimplifies reality, and removes us from each other. It thereby diminishes our ability to make progress in understanding one another and the world around us. While liberals tend to be the most outspoken about social injustices, it seems to me that they are also the least apparently embedded in those structures of society. Perhaps the one is on account of the other. Those embedded in structures are both most invested in their being good, but also possess the most power to do something about their being bad. Those who stand outside of them can only yell at those within them, and this, too, only creates division and polarization.
If we continue to advocate reform from without, we will continue toward revolution, the most extreme form of external "reform". If we desire change without unrest and disturbance, we must enter the very vilest of structures and change them from within. For this, a BenOpish solution may be necessary as a HazMat suit in order to resist the corrosive affects of those structures while we remove the corrosion.