Effective data visualization requires not only technical proficiency but also a deep understanding of the domain-specific context in which data exists. This context often includes tacit knowledge about data provenance, quality, and intended use, which is rarely explicit in the dataset itself. We present the Data Therapist, a web-based tool that helps domain experts externalize this implicit knowledge through a mixed-initiative process combining iterative Q&A with interactive annotation. Powered by a large language model, the system analyzes user-supplied datasets, prompts users with targeted questions, and allows annotation at varying levels of granularity. The resulting structured knowledge base can inform both human and automated visualization design. We evaluated the tool in a qualitative study involving expert pairs from Molecular Biology, Accounting, Political Science, and Usable Security. The study revealed recurring patterns in how experts reason about their data and highlights areas where AI support can improve visualization design.