Argumentative skills are central to persuasion, problem-solving, and self-advocacy, all abilities connected with developing a critical and personal perspective on information. Despite their relevance, argumentative approaches are not always systematically integrated in Higher Education (HE). This research examines the case of Italian HE institutions by analysing the syllabi of 133 courses from 47 public universities through stratified random sampling. The analysis investigates the presence and relevance of argumentative skills across learning objectives, teaching activities, and assessment practices. Findings revealed a limited and often fragmented inclusion of argumentative skills, frequently reduced to general comprehension and communication abilities, with weak alignment across curricular components. While references to argumentation are present, they often lack depth and coherent pedagogical integration. These findings point to the need for a more intentional and structured approach to developing argumentative skills, including a reconsideration of current curriculum design and a clearer integration and alignment of argumentation and critical thinking within teaching and assessment practices.