Frequent and recent debates on the ongoing political football that is abortion politics in this country are clearly the most obvious portion of how to tackle a dilemma. If there are others, they have much fewer muddled moral components (global warming to me is the closest national policy issue with the same lack of clarity in its debated terms). Most people generally accept a premise that abortions should be legal, but rare. That is, that they personally feel uncomfortable or wrong about them, probably wouldn't want one, but don't see a reason or way to make that discomfort into a preventive measure against anyone else wanting abortions. They don't articulate why they should be acceptable, or why they shouldn't. Even defenders of abortion rights do not tend to do so with a full-throated power that presents abortion, or even the option thereof, as a moral good in and of itself. What they do instead is present the portrait of people who oppose abortions as Luddites who hate women. This is likely true, given the ancillary features of the pro-life movement and its positions on issues like birth control or health care or economic gender balance, and so on. But it fails to present any moral ground on its own for women, other than to denigrate opposition. Better defenses argue the importance of existing, living, breathing, women and their rights as superior to the supposed or inferred rights of primitive embryonic beings that women would be otherwise gestating, or question the validity of these being counted as "beings" worthy of rights in the first place. Similar problems exist where pro-life/anti-choice proponents expend large amounts of effort portraying abortions as overwhelmingly late-term decisions of irresponsibility rather than the normally early term difficult dilemmas that they are in fact.
Let us suppose first the examination of certainty in claims. I think there are two basic claims of certainty: that a fetus/fertilised collection of cells, is affirmatively a human being, or that this is not. Science would seem to cut toward a notion that mere fertilisation and early development of a fetus is not necessarily viable human life given the extreme frequency of natural failures for such things to result in sustained human life (miscarriages, failure to implant in uterus, ectopic pregnancies, etc). Biblical logic, such as it is, also discounts these "lives" as invalid or at least uncertain. It is unclear on what basis the alternative determinations of certainty are made other than that they are a shared opinion or a deference to the creation of life as paramount for existence. A clear case can be made that claims of certainty for this being being a human with conferred legal benefits are horribly invalid assertions as a result. There is not however a clear case to state affirmatively its opposite, that personhood, or whatever value we assign to human beings, does not or should not be applied to its potential. Or at least, there is not a strong case, the case being that we should assign value to existing human lives, that of women, than their potential for producing progeny, not that their progeny should attain no moral significance.
This cuts against the legal and political value we assign to this issue being very useful, but it does present the necessity of individuals wrestling with these as options, and for social policy, if it is concerned at all with this issue, being aligned with the goal in mind of making it increasingly less likely that very many people do feel such questions as a necessity.
Here is the problem with debates over the certainty of life and personhood, the boring metaphysical premises that always raise their heads in any debate over abortion. It distracts from the actual decisions that must be made by real human beings. I find the debate over global warming or climate change and the required levels of certainty of knowledge and risk to be similarly useless. The real world problem is much simpler: generating energy for homes, cars, and industry, has actual real world costs that are not always being properly captured (pollution, health care, deaths of miners or floods or from lung problems, damage to ecosystem) and focusing massive attention on these would assert powerful political reactions as necessary. In other words, these are real world risks that we have greater certainty over than the potential for massive scale global climate distortions and the hazards these would present as necessary to avert (this is to say nothing of whether this risk is significant, I think it is, or what costs should be paid to avert said risk, which is much less clear). Similarly, in the case of abortion, there are real people who are wrestling with the difficult dilemma of what to do about their pregnant status.
The difficulty of abortion politics obscures that the penultimate question is "why". Why are people having them, what causes a demand? There is little value in asking things like "what value is there to human life or potential human life or their relative balance" so long as people have a desire to terminate pregnancy for some reason. At the ultimate answer we could arrive at is something like "because they don't want to be pregnant", usually for very circumstantial reasons (age of potential mother, health of fetal development, health of pregnant woman, financial constraints, already have other children/family planning efforts, etc). Any attempt to reduce this demand must provide methods of reducing the supply of unwanted pregnancies. This makes it, ultimately, an empirical question of which methods are most effective at this task. Although it is hardly a very simple and easy empirical question of things like "what improves women's educational or occupational opportunities such that their being pregnant does not impede career or life goals" or "what means can we use at a social level to decrease unwanted pregnancy". One of the most obvious responses is to increase access and availability and use of birth control by both men and women. I don't think the administration made a good enough push to do this by making birth control a non-prescription medical procedure and drug and went out about instead in the hamhanded way that most of our health care is delivered instead. That said, there's less of an actual link between access to birth control and demand for abortion than is presumed. It is very strong, but asking women why they are seeking an abortion generally produces a much smaller number of people who lacked birth control. Many women lacked proper use of birth control, which is an entirely different problem than accessibility (training). As a result, less obvious responses are things like using broader sexual education, supporting adoption, providing access to good neonatal care and information on how to wade through the difficulty that is a pregnancy, a relative tolerance for the native sexuality of teenagers, an understanding that there is no casual link between birth control access and the formation of desire and action of our basic sexual natures, and so on.
We see as a consequence why this becomes a massive political football. It has tendrils in various pies, and is a culture war nightmare for conservatives (watching their kids get instruction on condoms, be able to acquire pills or emergency contraception through a pharmacy without parental supervision, no longer can they pretend to have ultimate control over their child's morals, etc). It is far from clear to me why these methods must become political, or that their preferences on how to manage the situation should be enshrined as policy, but I think we should at least acknowledge that they share a concern over a similar dilemma. Even if their methods are basically outdated and useless or based upon deliberate misinterpretations of shared facts surrounding that dilemma.