Apparently there is an ongoing kerfuffle involving whether there is any secular argument to be made against any form of abortion. It seems worth pointing out here that the most thoroughly secular societies on the face of the planet have all enacted at least some legal constraints on when abortion may be performed upon request without specific medical justification:
In the United States we have a crazy quilt of state laws, many of which are designed push back against Roe v. Wade, subtly or unsubtly, and the public debate here is heavily faith-based on at least one side. Let us not assume, however, that as the U.S. becomes more secular that this particular line-drawing problem is just going to go away. There are humanistic concerns driving the squickiness that most people have towards third-trimester terminations; even after we manage to eradicate faith-based policymaking, we are still going to have these arguments.