Are there any (good, interesting, significant, etc) secular arguments against abortion?

Probably the most well-known secular argument against abortion is by Don Marquis. The paper is called Why Abortion is Immoral (sorry I don't have a link to a non-paywalled version) and the argument goes roughly like this: Start by asking why death is a misfortune. Marquis' answer is that it cuts us off from all of the potential value in our futures. This is why it's worse than being robbed or injured. At least if I'm robbed I still have the hope of a worthwhile future, even if that future has been diminished in some ways. But a fetus is a being like us in this very respect: other things equal, it has a future with a potential for value of the very same kind that makes death a misfortune for beings like you and me. This is true even if we believe that the fetus isn't yet a person. And so ending the fetus's life does it a very great wrong: it robs the fetus of the possibility of a valuable future in just the way that killing your or me does. In short, abortion is wrong for exactly the same reason...

Some people argue that a 15 year old should be required by their parents to have an abortion because they also can't get an ear piercing or attend an R rated movie without their parents permission. Is that a good argument?

Not sure who these people are, but the argument seems odd, and I'm not sure it's phrased to capture what you're really asking. As written, the question, is about whether parents should be able to require their (pregnant) children to have abortions. The supposed reason for saying yes is that for things like ear piercing, the child needs permission. That would be a strange argument. The fact that some things require permission doesn't tell us that other things can be required. If this is really what's at issue, the obvious reply is to offer a related but different argument: parents can require their children to do things they don't want to do. Therefore, parents can require children to have abortions. Now we see a different problem: the fact that parents can require their children to do some things doesn't tell us what the limits are. Take the ear-piercing case. It's one thing to say that a minor child needs permission for an ear-piercing. It would be another to say that a parent should be able to...

If it is illegal for a rape victim to kill the rapist after the fact, then why should it be legal for the rape victim to kill a baby that is the product of the rape? It seems to me that abortion is "vigilante justice" in a sense. This is all assuming, of course, that the unborn child is considered a living, human being. If it isn't, then why is an unborn child not then considered "evidence" to be used by a third party? I do not think an unborn child should be considered anything in between a "living human" and an "object," but please take this distinction into consideration.

My co-panelist has drawn some genuine distinctions, but I'd expect many people to find his response unconvincing overall. One obvious reason: suppose I have a five-year-old child who poses a very substantial burden to me. Perhaps the child has a physical disability that makes extensive demands on my time and money. Most of us don't think this would provide even the slightest justification for killing the child. And unless I could be very sure that the child would be cared for, it doesn't even provide a justification for abandoning the child. Now the analogy isn't perfect. After all, the rape victim is in no way responsible for the fetus. I may have chosen to become a parent; I may have accepted responsibility for the child. But even if we grant that those a re relevant differences, they don't seem to get us very far. Suppose the child wasn't mine but had been abandoned on my doorstep. It's hardly clear that this would make enough difference to justify killing the child or abandoning it once more. ...

Is it rational to both maintain that abortion is entirely morally permissible (on the grounds that a fetus is not a person, let's say) and to regret having had one?

There's no obvious inconsistency. The fact that something is morally permissible doesn't mean that there's never any reason to regret having done it. To take a very different sort of example: suppose I'm very busy, and I pass up an opportunity to go on a trip to some intriguing place, deciding instead to stick to my work. I might end up regretting my decision, even though it wasn't wrong of me to decide as I did. I might come to think I missed out on a valuable opportunity and that it would have been worth rearranging my work for the sake of it. Perhaps this doesn't quite get at your worry. Perhaps what you have in mind is someone who thinks that abortion is morally permissible, but who come to have moral regrets about having had one. That sounds more like some sort of inconsistency, but it needn't be. If the thought is "It was morally permissible for me to do this, but it was wrong of me to do it," then perhaps we have an inconsistency. But it's possible to think that something is permissible...

The moral question of whether abortion is wrong is whether or not it is a person. Well, I don't understand why people say that a fetus is not a person. How are a fetus and an infant any different. An infant doesn't understand the future just the way a fetus doesn't. At 14 weeks a fetus begins to move and "explore" the womb and itself. That shows some curiosity and some sort of "thinking". On a genetic level or the form of the fetus also at 14 weeks it is "a person". So then at the very least shouldn't abortion be illegal after that? If we should not kill an infant, which is very illegal, why can we kill a fetus which in many instances is on the same level as the infant? If anything we should not kill the fetus because it is innocent and the infant is not. An infant cries just to be held where it should cry because it needs something. Just as a small example.

It's been famously argued -- both by Mary Ann Warren and by Michael Tooley -- that an infant isn't a person either. The rough idea is that to be a person, a being needs to have at least a rudimentary understanding of its future that even a small infant still lacks. The point isn't to endorse that conclusion, but rather to point out that the premise of your argument -- that an infant is a person -- isn't universally accepted. That said -- it's hard to make the case that there is a difference in the moral status of a late-term fetus and a newborn (though that doesn't settle the abortion issue by itself.) But if we allow the term "fetus" to include early stages of pregnancy, then the further back we go, the more glaring the differences become. When we reach the point of a newly fertilized ovum, we have a gulf that one philosopher pointed out (sorry; I forget who) is quite stark. Some people insist that the conceptus has the full moral status that you or I have. Others can't even imagine what it would...

How can abortion be so easily accepted in a civilized society? Sure, it is important that a woman or any person be able to have control over their body, but the fetus is a separate entity, a new person completely, as is logically shown by the fact that a mother can give birth to a male child. Anyone can tell this without having to use the available scientific evidence which proves my point. So, what gives any person the right to kill someone else so that they can live the way that they want?

There are plenty of hard issues about when and whether abortion should be allowed, but the particular argument you're offering won''t work. You seem to be saying: a typical newborn is a person (I take that to be the point about giving birth to a male child) and you go on to conclude that a fetus is a person. But this simply doesn't follow. It's perfectly consistent to think that, say, a two-week-old embryo isn't a person, i.e., a being with the same sorts of rights that you and I have, even though other things being equal this embryo will eventually become a person.

When there is no clear solution to an issue, it would seem to me that assessing risks would be the most reasonable way of dealing with it. In the case of abortion we risk a mother losing the civil right to address her pregnancy within her own moral reasoning, verses a child losing its fundamental right to live. The latter risk seems more pressing and with greater consequence. Can a struggle for justice be assessed upon risk?

You've raised an interesting question. The general approach you're suggesting sounds like a version of what's called "multi-attribute utility theory." Without going into detail, multi-attribute utility theory lets us make decisions even when different sorts of values are at stake. Acting in a certain way might carry a high risk of losing money, but a high likelihood of keeping a friend. Depending on my "trade-off weights" (roughly, how much I care about money vs. friendship), and depending on the possible results and their probabilities given various choices, the tools of multi-attribute utility theory might give me a way of picking a course of action. It seems at least plausible that we could reconstruct any rational way of making decisions within this framework, and so in principle, we might be able to represent the way we think about the case you've offered. But this is really just where all the hard questions start. The first problem is that different people will weight different values...

Many people reject the death penalty on the grounds of mistakenly taking the life of an innocent person. Why then do we allow abortion? If no one is certain when life begins, isn't to accept abortion an acceptance of mistakenly taking the life of a person?

I sometimes call this the "Ronald Reagan argument"; President Reagan was fond of a version of it that, as I recall, had to do with a man in a ditch who might or might not be dead. That also raises a preliminary issue. The question presumably isn't whether the fetus is biologically alive; it surely is. The question (or part of it anyway) is what this living being is. One common way of putting it is to ask whether the fetus is a person -- a being with the same moral standing as you or me. And so I'll put what follows in those terms. The first thing that strikes me is that there's a glitch in the analogy. In the execution case, the being we execute is unquestionably a person who is possibly innocent. In the abortion case, the being is possibly a person, though if a person, then an innocent one. This hardly settles the matter, of course. The reply might be that in either case, we run the risk of taking the life of an innocent person; the position of the word "possible" simply locates...

As regards the point at which we should accord rights to that which would eventually be a child (an embryo, a fetus, etc.), does someone who argues that a given stage is not sufficiently mature have also to answer the question of which WOULD be the critical stage? Or is it enough to say, "Well, I don't know when this thing becomes a person, but it's not a person at day 1."

I think we can leave aside all the heavy-weather issues about abortion, fetal rights and so on and go for a more general point. It's hard to see why we'd have to have a sharp answer to the question of when something acquires rights or becomes a person, or becomes depressed or becomes fluent in a language or for that matter becomes a tree, or becomes bald... for it to be okay to say: "It's not there yet." In fact, there may not even be a sharp answer to the question "What is the critical stage?" Of course, if someone had a reasonable argument for saying that an embryo is a person from day one, we'd still need to evaluate what they had to say. But they would have to do better than point out that we don't have any way to draw a bright line between person-to-be and full-fledged person.