Perhaps... but birth is at least a bright line with a clear definition, and people are less likely to fear a slippery slope. If 'post-natal abortion' was allowed, I think people might fear a slippery slope where the deadline got later and later (and if it wasn't met with condemnation, some governments might even try to push the deadline out late enough to be oppressive).
No one would really know about or have reason to fear getting killed for at least a few years after birth at the earliest...