In the wake of COVID-19, enthusiasm is growing for hybrid and other blended forms of teaching. Before celebrating the hybrid future of education, however, it is instructive to interrogate its hybrid presence. Accordingly, this article explores pedagogical challenges prompted by the pandemic pivot to online teaching. Analysing qualitative survey data from Danish university teachers (n = 488), we identify five critical stances towards educational technology: (1) technologies are fine when used correctly; (2) technical issues are a major obstacle; (3) hybrid teaching is overwhelming; (4) one's sense of students suffers online; and (5) students hide behind their screens. Based on these results, this article identifies two challenges for the hybrid future of education: the problem of presence and the webcam-related tension between surveillance and care.