'Synchronous hybrid teaching' (SHT), defined as the concurrent delivery of online and in-person teaching, is an instructional mode employed by many schools during the COVID-19 pandemic to minimise learning loss for students who had to self-isolate at home. Since then, there have been calls for SHT to be retained as an instructional strategy post-pandemic to enable students who would otherwise miss school (e.g., students with certain mobility issues, health conditions and/or family circumstances) to still attend classes. To explore the feasibility of this proposal, this qualitative study drew upon the SHT experiences of primary and secondary teachers in different parts of Europe. The findings indicate that SHT is a demanding mode of instruction, one involving four different types of challenges: co-ordination challenges, administrative challenges, interaction challenges, and engagement challenges. More importantly, they demonstrate that SHT can struggle to consistently provide on-site and remote students with comparable learning opportunities and experiences. Through exposing the challenges involved in SHT, the study identifies directions for improving the quality of SHT in the future. It also calls for SHT employed during the pandemic to be referred to as 'emergency SHT' rather than merely as 'SHT'.