Dang I take forever to respond...
What has rights? A person, right? What makes a person? Not human DNA, obviously - human ears aren't people. Nor are brain-dead humans that still have functioning organs. Aliens could also be people. So something being "alive" or "human" doesn't make it a right-bearing entity. But what exactly is a person?
I'd argue that personhood is the result of sapience (sentience, self-awareness, consciousness, et cetera). And what is a necessary attribute for sapience? The ability to think and perceive. AFAIK, fetuses cannot perceive, sense, etc. until they are ~30 weeks old. (This might be smaller; at week 27 fetuses can operate their limbs and such, but still... there are a few months of pregnancy before fetuses can be said to be sapient.)
So...to continue the point here - why does a "person" have these rights in the first place? Why does sapience have anything to do with it in the first place?
Where do we draw the line? I could see the argument made that we shouldn't perform abortions on 37-week-old fetuses, but that doesn't really happen (save for medical reasons). Most abortions happen in the early months, far before fetuses can sense or move.
So you'd be ok with killing brain damaged people if they can't think or perceive any more? I admit that's a bit devil's advocate - but is there a difference? Why would you make a such a difference? I'd argue that it's just to make ourselves feel better, which isn't a really good reason. Is the entire difference the fact that a growing baby requires a host mother? Here's a thought from dystopian sci-fi: why don't baby's rights outweigh the mother's? After all, the whole purpose of the mother is so the infant can be created, isn't it? (Selfish gene theory and all that jazz).
Is something being killed? That's also debatable - fetuses act as "parasites", mostly, until the latest part of pregnancy. Not in the "augh infection kill it with fire" sense, not an emotionally-loaded term, just describing how they are not viable. But what if you don't consider them to be "parasites"? Are they a "bud" of the mother? I disagree - fetuses are separate organisms, so yes, something is being killed.
But we kill animals, we kill bacteria, we kill plants. Killing isn't in and of itself bad. Murder is bad because it's killing people. Killing animals might be bad because it is killing entities with the ability to perceive and (somewhat) think. Embryos can't do either.
Developing humans can perceive really quite early on actually. So what's the threshold? It shouldn't be arbitrary, but how do you pick? Is the whole argument because an embryo is inside a woman it shouldn't matter? Or I'll go back to this - why does sapience matter as a criteria? And if sapience does matter - why does it matter if a creature has sapience or is a creature capable of developing sapience had it been left alone for a few months or if it was sapient and lost sapience due to age or disease or accident?
Furthermore, abortion is a difficult decision. You don't have mothers thinking "eh, I'll just pop off to the doctor's and murder this baby in me." Why should the government do this - if the embryo is not a person, which it isn't, why should the government control and limit a medical procedure?
Wait what? The government controls and limits all sorts of medical procedures. And what does the "difficulty" of the decision have to do with it?
Birth control is equivalent to stopping people from having sex is equivalent to early abortion. They all prevent a human life from forming. Is that undesirable? Perhaps. But it is the choice of the mother, just like it is the choice of the mother to not have sex, and its difficult one. She doesn't need the government to tell her how to choose.
I don't agree with that equivocation. There is at the very least a significant chemical and physiological difference between failure to fertilize an egg and abortion. In a more "person" sense there is a difference between "I don't want to become pregnant, so I will take precautionary action" and "I think I might have become / know I am pregnant and I don't want to be."
Also what about the fact that a man can try to ensure pre-conception birth control equally as a woman, but cannot (legally) compel a woman to have or forego an abortion?
And sometimes it's for medical reasons, or rape.
So medical necessity is actually a rarity, and it the one situation where I would personally have trouble making such a decision, and I don't envy anyone who has to make such a decision.
Regarding violent situations: I can understand why someone would make that decision, but I disagree with it. My sentiment on that one is about the same as if someone chose to take up heavy alcohol consumption after some similar traumatic event - I can understand it, but not support the action.
Suffice it to say - the entire subject of abortion is just a mess because of the inability for humanity to agree on a fundamental basis for deciding "when an embryo deserves protection"; so the best we get is majority opinion often with a very vocal minority.
RANDOM: They must put something in the water for aerospace people. Like @Wierd I also have aerospace roots. Uncanny. (Mine was doing aircraft engine controller electronics and software design.)