People use arguments to justify their claims. Computer systems use explanations to justify their conclusions. We are developing WOZ, an explanation framework that justifies the conclusions of a clinical decision-support system. WOZ's central component is the explanation strategy that decides what information justifies a claim. The strategy uses Toulmin's argument structure to define pieces of information and to orchestrate their presentation. WOZ uses explicit models that abstract the core aspects of the framework such as the explanation strategy. In this paper, we present the use of arguments, the modeling of explanations, and the explanation process used in WOZ. WOZ exploits the wealth of naturally occurring arguments, and thus can generate convincing medical explanations.