Visualization has been deemed a useful technique by researchers and practitioners, alike, leaving a trail of arguments behind that reason why visualization works. In addition, examples of misleading usages of visualizations in information communication have occasionally been pointed out. Thus, to contribute to the fundamental understanding of our discipline, we require a comprehensive collection of arguments on “why visualize?” (or “why not?”), untangling the rationale behind positive and negative viewpoints. In this paper, we report a theoretical study to understand the underlying reasons of various arguments; their relationships (e.g., built-on, and conflict); and their respective dependencies on tasks, users, and data. We curated an argumentative network based on a collection of arguments from various fields, including information visualization, cognitive science, psychology, statistics, philosophy, and others. Our work proposes several categorizations for the arguments, and makes their relations explicit. We contribute the first comprehensive and systematic theoretical study of the arguments on visualization. Thereby, we provide a roadmap towards building a foundation for visualization theory and empirical research as well as for practical application in the critique and design of visualizations. In addition, we provide our argumentation network and argument collection online at https://whyvis.dbvis.de, supported by an interactive visualization.