You sound like a reasonable person and I respect your views. It's nice to discuss with a anti-abortionist who doesn't make knee-jerk statements. I agree it's not good to use abortion as retroactive birth control. Perhaps where we differ is that I don't consider "where human life begins" to be a useful yardstick in the debate. Neither do I think it's self-evident that "life" begins at birth or even that "life" is a very useful word in this debate.
I don't think saying "life begins at conception" is that helpful because, apart from anything else, about 25% of conceptions end up as miscarriages. So biology itself is telling us that conception is far from a assurance of an eventual new organism. Perhaps because I'm a biologist I see the word "life" very mechanistically and I don't understand how it relates to abortion, which is an ethical issue. I see when the fetus starts to feel pain as relevant, for instance. But at which point it is "alive" just isn't useful to me because that word encompasses far too many things and states of being.
I think it's too black and white and too easy to say conception==life and therefore life==human being and therefore abortion==killing. I see a human embryo is a potential new human existence (I'll avoid the word "life"). However, what it actually is at the time of abortion is anything from an undifferentiated ball of cells ball of cells to a highly undeveloped embryo that has nothing in common with a person. So when I think about this issue I think about it in terms of what the embryo currently is, not what it might become. I don't see it as "killing a person" or "taking a human life" I see it "as removing a ball of cells" or "removing an embryo that is currently indistinguishable from a chicken embryo". Of course later term abortions begin to become very unpleasant and there would come a stage in pregnancy where I'd probably be averse to abortion for anything but health reasons. I don't have an opinion as to where that line is, though.
In any case, my main point is that none of the above should be a major influence on politics.