First, I should probably say that I enjoyed the book. The following are a few criticisms, but I'm still glad I read it.
I don't want to spend much time on this, since others have covered this more thoroughly, but his explanations do tend to get repetitive and several of his "reasons" are variations on the same thing. If, for instance, a person rejects the notion that "because everyone else can be (and most people are) wrong about the religion they subscribe to, I could also be wrong", then many of his arguments fall away. In my experience, the cognitive dissonance required to reject that concept is perfectly common and once it's there, many of the arguments in the book simply lose any ability to get through to someone.
My greater issue with this book has to do with tone. While I understand what he is trying to do, I don't think it comes across the way he intends. At least, it doesn't come across that way to me. People are fond of criticizing the so-called "New Atheists" for being too harsh or too mean in their approach and that may be true, but at least it's honest. It treats people as if they are adults who are perfectly capable of defending their point of view.
The approach that Harrison takes, the "be nice about it" approach, may seem to offer a gentler, more reasonable alternative, but it comes across as entirely too patronizing for my taste. It reads like a man patting people on the head and saying "There, there. Just because the beliefs you hold most dear are stupid, it doesn't mean YOU'RE stupid." The effect of this is to infantilize people. It treats them as if they were either foolish children or else morons.
The direct approach may not pull punches, but at least it treats everyone as if they are expected, as adults, to be able to justify their position or surrender it.
Besides, when it comes to virtually every believer I've had contact with (and there have been a great many having been raised in the Bible Belt), it makes no difference. The religious folks I have known would not put this book into a different category from, say, Christopher Hitchens, even if he is nicer/patronizing about it. It has no greater chance of getting through to them just because he goes so far out of his way to pretend that he's not challenging their most basic beliefs. There are no brownie points to be had.
Then again, who knows what approach will work in the case of any one individual out there.