Here is what I think is the essential pro-life argument.
1. Either we are persons, having the right to life from conception, or we acquire the right to life somewhere between conception and birth, or at birth.
2. If we acquire the right to life between conception and birth, the criteria by which we become persons is arbitrary. We end up picking a point where personhood commences without an adequate reason for placing the point there.
3. But the right to life is not to be decided arbitrarily. The beginning of personhood must occur at a principled, not an arbitrary point.
4.The only principled point at which personhood can begin is conception.
5. Therefore, humans in the fetal stage have a right to life from the moment of conception.
6. The right to life has priority over other rights, both our own and those of others.
7. Therefore, we have a right to life from conception that has priority over other rights (such as the right to privacy, or the right to do as one pleases with one's own body).
8. If we have a right to life from conception that has priority over other rights, then abortion, except in those cases where the mother's life is in danger, should be outlawed.
9. Therefore, abortion should be outlawed in all such cases.