The conditional analysis of dispositions (CAD) is a major position to analyze dispositions, in which counterfactual conditionals are used. The advocates of CAD indicate that CAD is an intuitively correct way to capture our common sense understanding of dispositions, along with its simplicity in ontology. However, according to recent research, CAD is shown unsatisfactory because it is challenged by many counterexamples. Many philosophers take that the counterexamples of CAD arise from the logical characteristics of counterfactual conditionals, so any theory which attempts to use counterfactual conditionals to analyze dispositions cannot get rid of the counterexamples. This paper aims to characterize how the counterexamples challenge CAD from the logical perspective, and tries to propose a possible solution.