This article is an intervention in a growing scholarly literature and debate on ecocide, genocide and their nexus aimed as much at the teaching of these issues as at their study and research. The context for this debate is what the Permanent Peoples’ Tribunal (TPP) has aptly called ‘the most persistent war of our time, and the most difficult to win’: a war which ‘is being waged against nature and the “peoples of nature” by large corporations supported by states and the minority who run them’. The article argues that despite indisputable advances, yet the genocide-ecocide literature still suffers from the same grave flaws that have been at the basis of the disastrous failure of the genocide field (both scholarly and legal-institutional) to give absolute priority to genocide prevention. Many of those flaws lay in the reliance on a legalistic rationality to produce definitions of genocide. The article outlines a very different perspective which, contrary to liberal definitionalism, will be attentive to ecocidal-genocidal processes, logics and structures – a perspective that I name, in the wake of existing scholarship, ‘logics of destruction approach’. An examination of a few ongoing ecocides-genocides which exposes the common logics of destruction underpinning each case will show the workings of this perspective. The article concludes with a reflection on the question of justice, true justice, and how it interpellates us, scholars and teachers, and indeed everyone, now that ‘the most persistent war of our time, and the most difficult to win’ is at its peak and the planet and its denizens risk destruction and extinction.