The author is trying to present a probabalistic framework for reasoning about the world. The issue with p-values is that they have a narrow band of utility, and can't really contribute much to the process of inference as a whole; you can say no to a nearly infinite number of absurd propositions and still not be able to say anything insightful about a system. On top of that, p-values are clearly not intuitive, as demonstrated by their widespread misuse.