We describe two well-established, practice-based Master’s programmes as examples of existing competence development opportunities for practitioners and how such links between theory and practice can be developed and taught within the Higher Education (HE) context. We hypothesise that learning from major failures is essential in linking theory with practice in both engineering and management education. We investigate how to train emergency response teams on coping with, and learning from, rare events; a major challenge to other practitioners in the fields of safety and risk management. Comparison is undertaken between two disasters—Hurricane Katrina in the USA and the relatively recent Grenfell Tower in the UK—using a balanced dual approach of paradoxes, a dichotomy. In this paper, we demonstrate the enhancement of both engineering and management education. This was achieved through using the two case studies to emphasize the relevance of incorporating advanced mental modelling approaches for root cause analysis in training and by comparing the two cases with respect to the black swan and black elephant concepts. It is recommended that future training has a balanced approach that encompasses the outlined features of dichotomies.