Why do you draw a distinction at 'being born'? That's purely a transition from one support environment to another.
Termination at birth is clearly 'killing a child', termination shortly after conception equally clearly not. At some point in time between the status changes. Almost everybody, including most American voters, agrees broadly with this and while they might disagree with where the cut off should be, agree there should be a cut off and terminations should be freely available before. It's entertaining to see someone so clear about their opinion, most 'pro-choice' extremists, cannot quite bring themselves to articulate it. And you find yourself at odds with Roe-v-Wade, which is quite ironic.
FWIW I think the Roe-v-Wade and Casey update were bad, because they created law that should have been written by legislatures in conjunction with medical and scientific advice and then tested for constitutionality. The court found a right to termination, which is fair enough, and that the state had an interest in the foetus, which is also fair enough, and then it tried to reconcile the contradiction. Properly a job for politicians accountable to the electorate.
FWIW2 we're on the way to similar controversy. The UK law needs revision to make it clear a pregnant woman has a right to a termination, and to bring the time limit back below viability. This would also bring the UK more into line with the rest of Europe, so I would expect wide support....