I believe the article cited in the diary entry,
"Abortion Rights: A View from MIT", and many of the subsequent comments, are missing the main rationale for abortion rights.
You see, we could have a very large discussion (and we evidently are) regarding what makes a living creature "human" or a "person", and at what point that threshold is crossed in embryo/fetus development. And I think such discussions are important. "Personhood" is relevant, although it's not central to the principle upon which abortion is legal.
Now, I will agree with this: the "Unborn Victims of Violence Act" is premised completely (or it should be) upon the status of the embryo or fetus as a "person". But it's also intended as a "wedge" to change the subject to something a little more to the anti-abortionists liking. And that is mainly why pro-choicers are opposed to it.
Put simply, abortion is legal because we have the right to control our bodies. In cases such as motherhood, such a right supercedes any right to life an embryo or fetus might enjoy, even if it is considered a human being and a person.
A close analogy will suffice. Suppose you woke one morning, and found that another person had been surgically grafted to you such that they depended upon you for life. The graft could not be removed without the death of the other person.
In such a case, both legally and morally, you would have the right to have the other person removed, as no one can be forced to serve as a life-support machine for someone else. The right to control one's own body in this case is tantamount, and the "personhood" of the other is irrelevant (though a lack of personhood might make us feel better about the whole deal).
"But wait!" some might say, "in the case of an abortion, the mother chose to have unprotected sex! doesn't that make her culpable?" -- to which I'd say let's add to our original analogy. Let's say, before you had received the graft, you chose to walk through a bad part of town -- a part where, according to newscasts, people were being abducted and receiving surgery which resulted in other people grafted to them.
So, in walking through that section of town, your behavior was undeniably stupid. But does it cause you to lose the right to control your body?
The law (and ethics) would say "no". Anti-abortion types would have to say "yes". In fact, they'd have to go further and eliminate the right to control one's own body even if one hadn't engaged in foolish behavior.
I'm not sure if the author of this piece was deliberately obscuring this basic principle or if he simply didn't get it. But that is the principle you have to overcome in order to oppose abortion rights. Understandably, it is a principle anti-abortionists would like very much to ignore.