Few studies have explored the difficulties that undergraduates encounter in peer assessment from the dual perspectives of feedback givers and receivers and framed them in terms of specific needs for student feedback literacy development. To address this research gap, this study explored the obstacles that Hong Kong university students experienced during peer assessment in a General Education course based on 51 retrospective journal entries and 21 individual post-journal interviews. The findings reveal that the participants appeared to face more cognitive difficulties when giving feedback to peers and more socio-affective difficulties when receiving peer feedback, which indicates their specific needs for feedback capacities and dispositions. To prepare students cognitively for peer assessment, teachers must build up students' evaluative judgment and self-regulation capacities. To prepare them socio-affectively for peer assessment, teachers should help students to realise the benefits of giving feedback and their active roles and enhance their resilience and volition.