I am, of course, an atheist; this means that I do not believe in the existence of an immortal soul. This is, of course, very important in this debate, and it's the reason why I believe that the majority of the anti-abortion movement is based on religious reasons.
The religious argument against abortion is simple; they believe that at the moment of conception, the now-fused cells are invested with the soul, and become a human being in the eyes of their god. I'll give the argument this much; it's internally consistent with the rest of their superstitions.
I think I overuse semicolons.
For those of us who do reject the existence of the soul - and science must do so, for no evidence of it's existence has ever been presented - the question is less straightforward. When does a fetus become a person? What, for that matter, makes a person in the first place?
I wish to state for the record, unambiguously, that I agree with the right of a woman to choose, regardless of the circumstances. It's her body, and while the fetus remains inside her, completely dependent upon her body for it's life, I don't get to decide. I will be leaving these arguments by the wayside in the following, but I do believe in them.
That being said, we return to the question; what makes a person a person? The only serious difference between us and the rest of the animal kingdom is our minds; our intellect, consciousness, and sentience. If there is no soul, where do such things come from? In the eyes of science, it's all biochemistry. I'm nobody's idea of a biochemist, but it's widely accepted that the makeup of an individual personality, as well as memory itself, is stored in the synapses, the connections between brain cells. Each cell is connected to a number of other cells; the more connections, the more complexity, and the more powerful the brain. This, then, is what makes us people, what makes us individuals. The specific synaptic connections that we have are unique, which is why we, as individuals, are unique. In short, it's our complex brains that give us those distinguishing traits from the rest of the animals.
Fetal brains, of course, do not develop instantly. This is the crux of my argument here. Looking at BrainMind, it says under the heading "FETAL BRAIN-BEHAVIOR AND COGNITIVE DEVELOPMENT":
Cognition has been inferred based on alterations in fetal heart rate (FHR) and habituation to airborne sound, response-declines to vibroacoustic stimuli, and what appears to be neonatal preferences for the maternal voice as well as melodies and stories presented up to six weeks prior to birth
Take note of that timeline; six weeks prior to birth. Halfway through the seventh month. That's really late, as only up to one percent of all abortions are performed after 20 weeks of pregnancy (citations [here] and [here]. In fact, going back to the first paragraph of the BrainMind article:
...by the 25th week demonstrates stimulus-induced heart rate accelerations.
This is the very first indication of anything beyond simple autonomic responses, the first time that an outside stimulus can be shown to affect a fetus in any way at all... and it doesn't begin until 25 weeks.
But does some form of consciousness, however rudimentary, begin before this? We're back to brain structures and synapses, again. The cerebral cortex is widely considered to be the site of the higher-brain functions. The fetal brain begins differentiating in the second month, but the cerebral cortex does not come into it's own until it separates into it's two lobes - during the sixth month.
So, in short, we have development of the higher brain coming into it's own at six months, and true proof of cognition coming at seven and a half months, both well after the 20 weeks that the majority of abortions are performed. The majority of those performed after this date are, sadly, performed on wanted babies and done for medically necessary reasons.
I realize that that was long, and full of jargon, but it needs to be said. A fetus does not have a brain that's well developed enough to argue that you're killing a person, a human being. It's a clump of cells. It has the potential to become a human being, certainly, this is irrelevant. Destroying a clump of cells, no matter the potential, cannot be called murder. It can't be murdered if it's not a person yet.