Barak, that's a conundrum I've worried over since college. Leaving religion aside, preservation of (innocent) life is paramount. Nobody wants to be killed, it's one assault we cannot overcome. So as an individual and as a society preserving life must be a paramount virtue. And bang you're right back to the question of when life begins. Some opine this, some opine that but nobody knows. If preservation of innocent life is truly a paramount virtue we can only say with certainty that it's at conception or sometime after, however conception occurs. Saying life begins sometime after conception is guessing. How comfortable can one be with that? Some propose that life ends when age-related dementia reaches some arbitrary point.

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I'd much rather see abortion dealt with through social stigma than through government action.

Me too, but I can say that about any homicide. I see a somewhat greater role for government (society) than you do. If preservation of human life is a paramount virtue, I believe it is incumbent on society to protect and assist those who cannot do so on their own.

(Yeah, super short version with a lot of holes. Books have been written...)

The key elements in human thinking are not numbers but labels of fuzzy sets. -- L. Zadeh

Which explains a lot.