But what really strikes me about the argument is that which concerns the second part of the subtitle. The part of their argument that concerns the first part of the subtitle is standard material, nicely organized, but nothing that anyone familiar with the topic has not heard before. But the part of their argument that concerns the second part of the subtitle is quite astounding. I actually wasn't intending to read the work except that the summary of this part of the argument took me utterly by surprise:
Furthermore, since the right to life is not the right to someone else’s body, fetuses might not have the right to the pregnant woman’s body—which she has the right to—and so she has the right to not allow the fetus use of her body. This further justifies abortion, at least until technology allows for the removal of fetuses to other wombs. Since morally permissible actions should be legal, abortions should be legal: it is an injustice to criminalize actions that are not wrong.
'Since morally permissible actions should be legal, X should be legal' is a baffling thing to say, since it is not generally true that morally permissible actions should be legal; all that is true is that if an action is morally permissible, some other reason beside the morality of the action itself is needed for making it illegal.
Part of the problem, which you find in many discussions of ethics, is not grasping just how weak 'X is a morally permissible action' is, and with equivocating between 'X is morally permissible in every possible case' and 'X is a kind of action that is morally permissible'. Kissing strangers is a morally permissible kind of action; a society could very well exist where you kiss people you don't know in order to greet them, and there would be nothing wrong with that. But kissing strangers is not morally permissible in every possible case; you might live in a society in which it would be invasive. And moral permissibility is weak, in any case; most things we do are morally permissible, many of those are not very good or are in some way morally unsafe (tending to, although not strictly requiring, something bad).
And even when morally permissible particular actions are not of the barely-acceptable kind, there can be reasons extrinsic to the actions as to why they should not be done. Consider, for instance, the tragedy of the commons. We have a common resource, which benefits people by being common; everybody has a right to it; no individual use is detrimental in itself, but some overall combinations of individual uses are detrimental. Everything is morally permissible in itself, but, depending on what other morally permissible things people are doing, some things should not be done. Even purely practical reasons can be a foundation for law. I suspect most people would say that we could sometimes make a morally permissible action illegal if it could be a contributing cause to something we all want or need to avoid; at least, most people seem committed to such a claim given the laws they support.
I've looked and looked in the book for any developed account of why anyone should accept their principle that morally permissible actions should be legal, and I have come up with a blank. Indeed, the entire part of the argument that concerns the legality question is very weakly and minimally argued; it seems to consist entirely of two parts, 'most abortion is morally permissible' and 'if we made illegal the sort of abortion that is not morally permissible, this would have (very vaguely described) bad effects'. The legality principle seems never to be defended at all.
A side note. It's always worth asking in these cases what ethical approach is in play; one regularly finds in particular discussions of controversial topics that people are gerrymandering an approach to get the conclusion that is wanted -- that is, that people are not, in fact, being consistent in their ethics. I am baffled at what ethical view is supposed to be presupposed by their argument. They are presupposing some kind of cognitivist view (they rule out basing conclusions on feelings, attitudes, and preferences), but it doesn't seem to be any standard cognitivism. The strict way they take the legality principle seems clearly inconsistent with any kind of utilitarianism, and also with any kind of positivist theory of obligation; the way they handle questions of rights and personhood is inconsistent with Kantianism and natural law theories of obligation; virtue-ethical considerations never seem to arise. Perhaps the authors have some unified view, but it is not at all obvious from the whole collection of arguments that they give, nor is it even obvious that they are in fact sticking to a single ethical approach.