We document experimentally how biased self-assessments affect the outcome of matching markets. In the experiments, we exogenously manipulate the self-confidence of participants regarding their relative performance by employing hard and easy real-effort tasks. We give participants the option to accept early offers when information about their performance has not been revealed, or to wait for the assortative matching based on their actual relative performance. Early offers are accepted more often when the task is hard than when it is easy. We show that the treatment effect works through a shift in beliefs, i.e., underconfident agents are more likely to accept early offers than overconfident agents. The experiment identifies a behavioral determinant of unraveling, namely biased self-assessments, which can lead to penalties for underconfident individuals as well as efficiency losses.