Even if one were to accept the idea that "abortions of convenience" should be forbidden, while quite obviously the termination of non-viable fetuses should not, we live in a real world, not one of theoretical perfection. And in this real world, the forbidding of one leads stupid and overly cautious people who consider the prevention of "abortions of convenience" their primary goal to acting against the interest of at least a few. People enforce the laws that people make, and some of the people who make these laws are profoundly ignorant.
It's likely, that as theprestige points out, we could all agree on the theoretical issue of abortions of medical necessity. Whether we could agree on the exact bounds of medical necessity is less certain, but let's forget that for the moment. If one supports the system now prevailing in those places where "abortions of convenience" are forbidden, then the theoretical issue remains only theoretical, because decisions are made by human beings, and the laws in many places are so severe that the penalty for allowing an abortion is greater than that for injuring or even killing an adult, and however few the errors are, they exist, and acceptance of those laws constitutes acceptance of that bias and that collateral damage.
In a real world where things are ambiguous, varied, and decisions subject to human error, there will likely always be some error, some level of collateral damage. As things stand now, it seems the fear of someone getting away with an unnecessary abortion exceeds the fear of someone being harmed or killed by the withholding of a necessary one. Of course it's easier for me to say, since I support abortion rights anyway, but for me, that's the wrong way around.