People who buy and follow the advice of the Pearls are likely to already be people who would resort to beating their children as punishment. Children being beaten to death happened before the Pearls published their book. Presumably some would still have happened regardless of the book being published. And they would have happened to people who are likely to beat their children, obviously, which are the Pearl's audience. So, it's perfectly possible that in a hypothetical universe where the Pearls never published their book, this same deaths happen to the same people, meaning that in fact the Pearls did not cause those deaths.
This. I have read
To Train Up A Child and I believe in corporal punishment and discipline. I don't agree with everything in this book and I do believe that the Pearls sincerely think that they are providing sound advice and have a desire to help parents raise their kids effectively. Now, one of the problems is that they wrote their book based on
their experience and their results and how it was successful for them and in doing so, wanted to share their techniques to the world. However, once they had their book published and put into the hands of the public, it is what the readers make out of it and how they implement his instructions. Some may be able to follow it within the guidelines and not cross the boundary of child abuse while others have gone overboard and actually harmed and even killed their kids. Those parents that stay within the reasonable boundaries are usually good parents and know that there are limitations on punishment. The other parents probably are the type that had an abusive personality in the first place.
In the book, Pearl often talks about not punishing your kids while you are angry but instead wait a few minutes and then punish them in a more calm and rational state of mind. I feel that many who have read this book and implementing the methods probably have punished their kids out of anger, causing more injury to the child. He also talks about discussing the punishment with the child afterwards, explain why and to let them know that you love them. IOW, I do believe that those that have gone overboard have probably skipped or forgot those parts.