Peer instruction is a method for activating students during lectures, which has gained a considerable amount of attention in higher education due to claims of dramatic improvement in learning gains. The purpose of this qualitative research study is to investigate what types of discussions engineering students engage in during a peer instruction session and what learning possibilities that are enabled by these different types of discussions. We observed twelve students during six separate and simulated peer instruction sessions and the students were interviewed individually after the sessions.Ananalysis of the data revealed that the students engaged in three qualitatively different types of discussions: affirmative discussions, motivating discussions, and argumentative discussions. We characterize these different types of discussions in terms of the number of alternative answers the students discuss, the extent to which they draw on prior knowledge and experiences, as well as the fundamental difference between an explanation and an argument. A good opportunity for learning is opened up when students are aspiring to find the truth, not simply being satisfied with what they believe to be true. We conclude that students do not always engage in discussions that support their learning in the best way, and we discuss implications for using peer instruction as a teaching method.