This is a tremendous can of worms any day that you open it and in any country where you try to open it.
On the one hand, I know that a woman in the situation of need to have an abortion is already in trouble (and I don't mean that in the euphemistic sense used 40+ years ago.) On the other hand, I'll never have to make that decision. I didn't have to in the past and now my wife and I are too old. For us personally, it is a moot point. In the USA, we have a few factors to consider. I'll try to enumerate them clearly enough to then use them as the basis for my position.
1. (Legal) The US Constitution is vague regarding the beginnings of life. However, it makes one (and ONLY one) reference in passing. Based on our constitution, civil rights apply to naturalized or natural-born citizens. There is no mention of potential life or developing life. Rights accrue at birth.
This is a back door, to be sure, but it sets a reference point of birth. Obviously, naturalized citizens must take an oath, which means they must already be born and in fact old enough to be considered to have the capacity to take an oath. So though it is at best an implication, the US constitution implies that life begins at birth.
2. (Religious) The US constitution and its amendments expressly allow people to expect the right to freely exercise the tenets of their religion. Religions vary on when life begins, from conception to quickening to severing the umbilicus to the first breath. (Yes, that wide a range.) As much as I study this, I can only come to the conclusion that setting an early cut-off point disenfranchises the woman who is practicing her religious beliefs and is a member of the crowd that believes "the breath is the life." Setting too early a cutoff point tells that woman that her religion is inferior. But the USA disallows any legal decisions to occur that make such an implied statement.
3. (Legal/Religious) In cases where the child, already born, must face a life-saving treatment but the parents' religion doesn't believe in medicine, courts have ruled that the parents have the legal right to deny such treatment. Insane though it is, I see that as proof that the parents have the right to decide to allow the life of that child to end even after birth, contravening the rights granted by the US constitution. Why, then, does everyone get MORE bent out of shape if the woman decides to stop the pregnancy before that situation could happen?
4. (Pragmatic) Before the US Roe v. Wade decision, abortions occurred in back alleys where young girls were maimed, killed, sterilized, and generally treated to an uncertain fate. Often, both woman and fetus died. By allowing abortions in a clinical environment, you save one of those lives. But you can't stop abortions. They've been around since the time of the Pharoahs. The Hippocratic Oath refers to abortifactants. Seems like we haven't gotten rid of abortions yet, after well over 3000 years of recorded history to the times of the Pharoahs.
5. (Pragmatic) If the prospective mother so badly doesn't want that fetus to become a child, how badly will that child be treated in life later? Based on typical outcomes, the child would grow up unloved, in poverty, or in an overloaded foster care system. The child would become a ward of the state, potentially unloved, exploited, and/or abused. People say, "Put the child up for adoption." Probably would be good except that the number of children far outnumber the number of prospective adoptive parents. I can't justify this number because I don't remember where I saw it, but I think I recall that the ratio is on the order of 8 to 10 abandoned children to 1 prospective adopter. So most kids put into the care of the state are going to foster care or orphanages.
6. (Legal/Pragmatic) The pregnant woman facing abortion is, more often than not, facing it alone. The sperm donor has already fled the scene (and probably bragged about yet another conquest.) Leaving the woman "holding the bag." She has no effective method to coerce his support because he can just leave the state or go into hiding. (See #7 point below.) This asymmetry of responsibility places the woman in an untenable condition where, no matter what is really the right answer, she is unlikely to make it due to the familial, societal, economic, and biological pressures placed on her.
7. (Personal experience) In the two cases where I know all of the details, the sperm donor who cut and ran totally abandoned the mothers, both of whom shouldered a terrible burden but eventually accepted the birth of the child. The children (both girls) suffered very difficult childhoods and grew up unable to make good choices for the men in their lives. One is my stepdaughter, whom I've tried to love as a good father. But it isn't always easy.
8. (Idiocy) In the USA, many schools are forbidden to use the words "birth" and "control" in the same sentence for fear that the religious extremists will storm the school and hang the principal. In effigy if s/he's lucky. Post-pubescent but uneducated children in "ripening" bodies can be described in simple terms - prime candidates for parenthood.
9. (Idiocy/Pragmatism) When someone says, "Just say 'NO' to underage sex" they are talking from a part of their brains that is detached from reality. Kids TUNE OUT the adults most of the time on a good day, so when an adult starts a lecture on the perils of sex, the kids hear BLAH BLAH BLAH. Adolescent celibacy is like jumbo shrimp and military intelligence. An oxymoron.
10. (Religious) Every Christian I've ever met claims the soul cannot be destroyed. If the fetus is terminated and had no soul (yet), then nothing much happened. But even if the fetus had a soul, termination if its host body couldn't destroy it. So what's the reason for the furor?
Having pointed out these relevant factors, I think abortion should be legal, but stronger legal and societal tools are needed to make the sperm donors take responsibility for their actions. I would prefer that we take steps to prevent the pregnancy before abortion ever becomes the issue.
Teach birth control and make sperm donors get serious punishment for starting an unwanted life. We would punish them for ending a life improperly, wouldn't we? I don't think any woman should have to bear a child she doesn't want, particularly under tough economic circumstances and sperm-donor abandonment.
I wish it were not this way, for I regret the need for abortion. And that is the dilemma. We hate the event but cannot eliminate the need. And eventually this is why I place myself in the category of saying that it is a woman's right. If it is a sperm donor's right to "love 'em and leave 'em" then it should be a woman's right to put that liaison out of her life and her body completely.
Stated another way: If we cannot prevent the condition, why do we then want to step in and compound the problem?
Rather obviously, I've studied this question at a deep philosophical level and still cannot come up with an answer that I like. It's that pragmatic streak in me, I guess, that says it doesn't matter how theoretically perfect your answer might be if it doesn't solve the problem.
