Conflict is an inescapable reality in contemporary life, and higher education (HE) is not immune. From armed conflicts to campus protests, university educators increasingly navigate volatile environments where teaching is intertwined with global struggles. Educators may face violence, displacement, or the effects of heightened militarization and censorship on campuses. As student movements advocating for peace and justice intensify, universities globally are witnessing growing tensions between academic freedom and state responses to perceived "controversial" issues, such as coloniality, human rights, and gender equity. Integrating insights from peace education (PE) and education in emergencies (EiE), the paper critically examines the role of HE in peacebuilding and/or conflict exacerbation. It raises four questions for university educators to reflect on as they teach about conflict and peace, exploring the essential role of HE in questioning and disrupting (or not) the essence of conflict and its relationships to violence, sustainability, and peacebuilding.