The United Nations 2030 agenda includes quality university education, highlighting the importance of writing competence, as a basic skill for the dissemination of sustainable knowledge. However, there is little evidence of the factors that predict effective written communication to support such quality. Among these factors, the literature highlights motivation and writing metacognition, as well as the adequate structuring of the academic and/or scientific genre. The main novelty of the present research is the study of the relationships between the mentioned factors, measured with validated instruments. To this end, content analysis is first applied to determine the rhetorical moves of argumentative essays written by a sample of 72 university students. Secondly, the correlations between each of the rhetorical moves, metacognition and argumentative writing self-efficacy are calculated. The relationships are studied in depth, applying step-by-step linear regression models. Finally, the dependence of the results, observed with respect to unmeasured factors, is contrasted by means of a confirmatory analysis based on structural equations. The analyses show that it is the practical ability to express rhetorical moves—Conclusion and Bibliographic References—which predicts a students’ writing metacognition. Moreover, the minor relationship that argumentative self-efficacy shows with the expression of rhetorical moves, compared to writing metacognition, point to the need to consider another motivational dimension that is driving the learning of the argumentative essay at university level, a hypothesis that is confirmed with the structural equations model. These, and other findings, allow for the establishment of a series of educational quality criteria for the empowerment of written argumentation in academic and scientific contexts.