I've written about this at length over the years, but I find this morning that search engines like Google and DuckDuckGo can't find anything I've written on the subject. So let's run through it one time quickly.
1) Abortion kills a living, individual, human being.
1a) Living: Philosopher
Hans Jonas points out that the activity that
is life, what makes a living being different from a rock, is that the living being is taking resources from nature and putting it into its own order. Your body does this all the time. You eat, your body digests the food and breaks it into constituent elements or molecules, and then puts those things into the order of your muscles, bones, organs. That's life. That's what life means; that's what life
is. A child is doing that from the moment of conception, dividing and ordering, taking resources from its mother to bring itself into the order that also
is itself.
Cf. Aristotle
Physics II.1: "Of things that exist, some exist by nature, some from other causes." That's what he meant too: the baby in an important sense causes itself to come to be ('by nature'), whereas the rock came to be because of forces not its own. Heat created magma, uplift created cooling, weather broke it from the earth and made it a rock rather than a part of a mountain. Life entails having a nature, an order of your own, taking from the world and putting a part of the world into your own order.
So: abortion kills a living being.
1b) Individual: The order that the being is putting itself into is its own. It is not its mother's, nor its father's. Even in the case of twins, quickly the orders begin to diverge from each other and are subtly different. The child is a unique being. The child is not you: the child is himself or herself.
1c) Human: Nevertheless, all children have an order that is recognizably human. It is genetically distinct and different from other sorts of beings, e.g. dogs or bats.
Therefore: It is proven that abortion kills a living, individual, human being.
2) Aborted children are usually innocent in the strict sense of the word.
2a) Innocence implies absence of guilt. As a rule, guilt is a matter of the will. The child's will, before birth, is in a minimal state of activity: the child can move about the womb of its own free will in the later stages, but for the most part his or her actions are informed by instinct rather than will. Growing, for example, is an act of the child but not a chosen or willed action.
2b) Occasionally guilt can occur accidentally. When a child's body embeds itself in an intratubal manner, the child through no act of will is going to be guilty of killing his or her mother. Other times, children die in the womb and cannot be ordinarily expelled. These children, likewise, are accidentally guilty of killing their mother through sepsis and the like. This is not guilt in the strict sense, but by analogy; but it is nevertheless the sort of thing that might license violence in self defense (see 3, following). If someone is accidentally about to kill someone, and there is not time or space to reason with them about it, you might reasonably use violence to stop them from doing so.
3) Usually violence towards another individual human being is only justified by defense of self or another who is innocent.
3a) From 2b, I can see limited cases in which abortion is fully justified. If the mother would die and, therefore, the child will also die, it is sensible to save the one life that might be saved. If there's a legitimate choice between saving either life but not both, the mother might sensibly defend her own life if she chooses to do so. This is not the position of the Church, please note; it is a place where I dissent from the Church's teachings for what I take to be honest and honorable reasons. I trust in forgiveness if I am in error.
4) Thought experiment A: The Deer Hunter
4a) Though it is here proven that the child is a living, individual human being, it is sometimes argued that we cannot really know if the child is a 'person' or not. This strikes me as a fiction created for the purpose of creating an ambiguity that might allow for an immoral action, exactly like 'race' was invented as a concept in order to create a class of human beings whose interests might be ignored for convenience. 'Personhood' separate from 'the category of being a living individual human being' is almost nonsense; it could in principle extend to aliens or some such, but even then it would still embrace all living individual human beings.
4b) However, consider the case of a person who has a duty to feed his family. Times are hard and they are hungry. He takes his rifle and goes out into the woods to hunt for food. After a long time, he sees movement. At that distance, though, he cannot quite be sure if what he is seeing is another person or a deer. It could be a deer, but it also might be a neighbor who is walking in the woods in a deer-colored coat. May he morally shoot what might be another person, being uncertain?
4c) He may not. If he fires and it turns out to be a deer, all is well; but if he fires, and it turns out to be his neighbor, he is guilty of manslaughter. Choosing not to fire, by contrast, is always guiltless.
4d) The needs of his family for food might be considered a mitigating factor in determining just punishment, but not a sufficient justification for the manslaughter.
4e) Therefore, uncertainty about the personhood of the child is not a defense for killing it. The only certainly moral choice in cases of uncertainty about personhood is not to choose to kill.
5) Thought Experiment B: The Artificial Womb
5a) Another defense of abortion that is sometimes made is that women should not be forced to harbor a child to term if they do not wish to do so. Consider -- as is not hard -- a technology that would allow the child to be safely transferred to an artificial womb, so that the woman did not have to carry the child if she did not wish. Would she still have the right to kill the child, if there were an alternative?
5b) I submit that her bodily autonomy would be adequately preserved if she were free to remove the child to an artificial womb. However, notice that in such a case she would still have duties to her child. Just as a father has to pay child support even if he is not otherwise involved in the child's life, so too would she -- equal rights, equal duties -- have to pay for the support of a child she engendered even if she did not otherwise wish to be involved with the child.
5c) The current status allows a pernicious inequality of rights and duties between men and women, by allowing women to dispose of the child and/or their duties to the child (many states have surrender points where a living child can be abandoned without questions), but requires men to be responsible for 18 years regardless of their choice. This is a basic unfairness in our legal structure.
5d) More, it violates natural law as regards the woman and the child. The purpose of traditional institutions like marriage is the recognition that humanity naturally produces children, and children by nature need to be supported and educated to adulthood so that they can assume proper places in society. Children are due this from their parents by nature. That is true for both parents. It is a natural duty that our society has for decades attempted to relieve for women.
Conclusion: Except in rare cases as provided in (3a), abortion is morally wrong. It ought to be dealt with accordingly.