It was an attempt to define a word to fit their personal agenda, which is exactly what you are doing. Further, the personhood argument is irrelevant. We don't allow people to kill cats for fun, or kill cats inhumanely for good reasons, even though they are not human, and whatever rights they have are creations of the law. Why? Because they feel pain.
So tell me, does a fetus feel pain when it is surgically dismembered at 7-9 months? If so, we need to examine the context of the abortion to decide whether or not it would be moral. If it means saving the mothers life, it would be moral. If it means a person would not be born to parents unable to take care of it, it would be immoral, as there are plenty of contraception available to just about everyone in the Western world. Thus my argument that the only sound justification for abortion is pragmatic; there is literally no way to justify the action in moral terms, outside a very narrow set of circumstances.
In conclusion, abortion is a necessary evil, because the actions needed to prevent such immoral abortions are as immoral as that which they would prevent.