In this short article, we pose six key questions that we argue as essential to critically problem-pose in achieving teaching for justice-based environmental sustainability (JBES) in higher education (HE). We will be critically posing these questions to all the authors of an upcoming Teaching in Higher Education special issue 'Higher Education Teaching of Environmentally Just Sustainability' so they can further unpack these questions, coincide or counter our arguments presented here, provide rich contextualization in their responses, and possibly expand upon these six. The questions problematize the following in HE teaching: (1) the (de)legitimized, (de)prioritized framings of 'sustainability;' (2) the same question for the terms of 'development' and 'sustainable development'; (3) the politics of (un)sustainability affecting HE pedagogies and curricula; (4) HE's roles and responsibilities in leading to students' praxis of sustainability; (5) the incorporation, or not, of Southern, Indigenous, and/or Northern epistemologies grounding (un)sustainability taught; and (6) the (non-)anthropocentric groundings in HE learning.