Can we have a civil discussion about abortion?

I'm undecided on the issue of abortion, and tend to want to argue against people with strong opinions on either side. To me the answer is unclear, so I'm frustrated by the strident views of many people on this site (and everywhere, really). I'm not trying to be adversarial, but rather bring up points that I haven't seen good answers to in hope of some enlightenment.

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1. At what point of fetus development, if any, does abortion become wrong? Why?

It seems that any answer to this question is arbitrary, and if you don't think that such a point exists, then why not be able to kill newborns? Nothing magical happens to the baby's physical development at the moment it leaves the womb, so why is killing a newborn any different than aborting one right before birth? (I'm just playing devil's advocate)

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2) Is it wrong to have beliefs that are morally based and not necessarily logical?

I don't think there's a correct answer to my first question which leaves me making a decision based on my moral feelings towards the issue. I don't think that anyone feels good when they see a late-term aborted fetus, but I also don't feel good seeing animals slaughtered, and I'm not a vegetarian. So are our moral feelings worth anything? And if they're not, why shouldn't I be able to kill a newborn? (again, just playing devil's advocate)