Chemists formulate theories and models to rationalize data and predict outcomes in new chemical systems. With prolonged immersion in these models and our intuition as experienced chemists, certain observed reactivities may appear 'more expected' than others. Unexpected reactivities often arise, manifesting as exceptions and/or paradoxes. Exceptions in chemical theories are ubiquitous and indicate an incomplete understanding, suggesting that the chemical system is not accurately described (i.e., the "boundary" that decides whether a reaction is relevant to the theory is not well-defined) and/or that the theory has limitations. Therefore, viewing exceptions not as anomalies but as opportunities to deepen our understanding is crucial. While the concept of scientific discovery described here is not new, it remains significantly underappreciated in the field of organic chemistry practically. Many long-standing problems remain stagnant because essential questions have not yet been asked. One key reason is that unexpected reactivities have been underappreciated. To address this, inspired from the logic of scientific discovery in general, I postulate some origins of unexpected chemical reactivities across different contexts, offering a possible systematic approach to dealing with paradoxes and exceptions that may facilitate continuous improvement of models. While the emblematic examples focus on physical organic chemistry, the concepts discussed are universally applicable across different fields in chemical science.