Background Despite continuous performance improvements, especially in clinical contexts, a major challenge of Artificial Intelligence based Decision Support Systems (AI-DSS) remains their degree of epistemic opacity. The conditions of and the solutions for the justified use of the occasionally unexplainable technology in healthcare are an active field of research. In March 2024, the European Union agreed upon the Artificial Intelligence Act (AIA), requiring medical AI-DSS to be ad-hoc explainable or to use post-hoc explainability methods. The ethical debate does not seem (...) to settle on this requirement yet. This systematic review aims to outline and categorize the positions and arguments in the ethical debate. Methods We conducted a literature search on PubMed, BASE, and Scopus for English-speaking scientific peer-reviewed publications from 2016 to 2024. The inclusion criterion was to give explicit requirements of explainability for AI-DSS in healthcare and reason for it. Non-domain-specific documents, as well as surveys, reviews, and meta-analyses were excluded. The ethical requirements for explainability outlined in the documents were qualitatively analyzed with respect to arguments for the requirement of explainability and the required level of explainability. Results The literature search resulted in 1662 documents; 44 documents were included in the review after eligibility screening of the remaining full texts. Our analysis showed that 17 records argue in favor of the requirement of explainable AI methods (xAI) or ad-hoc explainable models, providing 9 categories of arguments. The other 27 records argued against a general requirement, providing 11 categories of arguments. Also, we found that 14 works advocate the need for context-dependent levels of explainability, as opposed to 30 documents, arguing for context-independent, absolute standards. Conclusions The systematic review of reasons shows no clear agreement on the requirement of post-hoc explainability methods or ad-hoc explainable models for AI-DSS in healthcare. The arguments found in the debate were referenced and responded to from different perspectives, demonstrating an interactive discourse. Policymakers and researchers should watch the development of the debate closely. Conversely, ethicists should be well informed by empirical and technical research, given the frequency of advancements in the field. (shrink)