I'm actively non religious and somewhat anti-abortion, at least late term. The argument really comes down to when life begins to me. I don't for a moment accept that it is at conception, but I do think it is before birth.
It would be murder to abort a child then kill it.
Prior to viability, an aborted child will die if < ~ 24 weeks (with rare exceptions and the most skilled intensive care, 21 weeks).
From 24 to 26 weeks most infants would not survive without medical intervention and a few would begin surviving without medical intervention from 26 weeks on however, they would still need special feeding because they cannot nurse sufficiently at 26 weeks.
I see no reason to not use the age of viability outside the womb as a guide regarding abortion and most clinicians who perform abortions are very reluctant to perform abortions on viable fetuses. But I also see no reason not to leave that decision up to the provider and patient. If you are presented with a 12 year old victim of incest who by circumstance did not bring their pregnancy to anyone's attention, the decision should not be based on an unforgiving law.
Pregnancy and childbirth are leading causes of death in teenage girls in developing countries. And while not quite as bad in the developed world, pregnant teens still have serious health risks.
Legislating medical care is wrong (I'm not talking about negligence and laws regulating practice such as licensing providers or drugs) Legislating morality is often worse. I see nothing whatsoever immoral by my standards in a woman seeking an abortion of a fetus that is the size of your thumb and is as developed as a fish. At 19 weeks the infant looks pretty much like a tiny baby but since the decision, as you say, is somewhere in between conception and birth, and one must draw that line somewhere, if one person draws the line at 18 weeks and another at 23 weeks, who is to say there is really any substantial difference.
Viability does at least define a difference. However, some people watching thousands die in poverty might find it equally immoral to watch a million dollars being spent saving one 24 week old preemie.
Pregnancy poses a very serious threat to the mother. We don't think about that danger because risk has been considerably decreased in the US and other well off countries.
Every minute, a woman meets her death during pregnancy or childbirth.
98% of the deaths are in poor countries, but when you have very young pregnant girls, the risks from the pregnancy are high even in countries with good medical care.
State of the World's Mothers 2006 (See page 11 of the report for some maternal mortality stats in the worst countries.)
But there are also deaths which do not end up being recorded as pregnancy related. From
a news article after the Lacy Peterson murder:
Homicide was found to be the leading cause of death for pregnant women in Maryland, according to a March 2001 study published in the Journal of the American Medical Association. Using death records and coroner reports, state health department researchers found 247 pregnancy-associated deaths between 1993 and 1998. Among those deaths, 50 were murders. By comparison, homicide was the fifth-leading cause of death among Maryland women. And, nationwide, the maternal mortality rate was just 9.9 percent in 1999, the most recent year for which statistics are available.
The point of this is that to decide on the morality of abortion by only looking at the issue of is it a child or a fetus is an immoral point of view in itself. Many people who have strong opinions against abortion simply ignore the fact this isn't a baby in a test tube. (The frozen embryos are, I'll get to that in a sec.)
Leaving aside confounding issues such as, is it one murder or two if you kill a pregnant woman, the real problem as I see it is trying to address this matter with laws, especially laws aimed at forcing one person's morals on another. It's one thing if the majority find murder immoral, but quite another if only half the country finds something to be immoral. To base a law on the moral opinion of 51% (give or take) of the population makes no sense. To have the legislators interfering in medical decisions between provider and patient in this case ties the hands of providers to give the best medical care they can.