These are all questions we'll run up against soon, and I believe anti-abortion people will have a huge problem with.
If your measure is capacity of reason, you can define a person by the complexity of its nervous system. For instance, if you don't have anything against killing rabbits, you could kill a fetus that is at that level of complexity. I don't kill rabbits as well, so, wouldn't be my preference, but as long as you have that measure, it makes sense.
I guess you could expand it to include being self-aware and feeling pain, too. Rabbits would qualify then. Conscious ones, anyway.
The "machine with the potential to think" problem is much easier for me. It's not on, so, you are not destroying any ongoing process. Not the same as abortion.
I would argue it's no different from killing someone who is asleep or unconscoious.
While at it, why not take another small step and question why capacity to reason determines value? Nothing apparent, other than the fact that it is an arbitrary point where social evolution took us (economical benefits of better cooperation, etc.). You could as well include animals and beings with potential of rational thought, or go the other way and exclude some human races, social classes, etc. It's all arbitrary from a personal point of view. Not against your opinion (makes sense to me too), just questioning where it's coming from.
The "why" would be because this person/being is able to make their own rational choices, and can chose to live. A fetus or an unconscious entity cannot. I think it's kinda close to the base libertarian or objectivist source or rights thing; I have a right to my own being. If someone can declare that, they have that right. As for animals with rational thought, pretty sure that's coming too, and if right-wing extremists had issues with blacks and gays, omg that will open a can of worms!
Suppose you have a sick person who has lost the ability to develop rational thought. You have means to fix this person. This man has the potential to do important things. Does this entity (I won't even call it a person, since it can't reason) have any value at all? There is some value because of the investment gone into developing this human of course, but let's say fixing has the same cost as developing a new person from scratch, so that we can exclude that.
I would say that no, this person does not have value by themselves. The development portion is a sunk cost at this point. If someone else values them, like a family member, or a business owner who knows that this person has a lot of potential talent as a future employee, then they can value them. If no one values them, then there's no point in their existence, which I assume would be at the expense of the state with nofuture fix options (unless society deems that people like that should be fixed, and votes to foot the bill, but in this case society is valuing them for whatever reason).
I think the main anti-abortion opinion in this thread stems from the idea that you don't have to care for any person. No person or entity has inherent value, it doesn't matter of it can reason or not. People are saying you can evict your child from your home without giving any means to survive as long as you make it public.
I agree with the eviction sentiment. If you make it public, someone else will step in and take that child.if no one does, then society may have way bigger problems than just abortion.
I have a feeling the main anti-abortion opinion stems from religious beliefs, that as soon as a sperm enters an egg and the two halves of the DNA mingle, god imbues the resulting cell with a soul, and at that point it's a human life, the killing of which is murder. Questions of what embryo or fetus souls would look like in heaven aside, I have a feeling a lot of them also have never really bothered to consider what really defines human life, worth, and consciousness.