Gesture recognition based on surface electromyography (sEMG) has achieved significant progress in human-machine interaction (HMI), especially in prosthetic control and movement rehabilitation. However, accurately recognizing predefined gestures within a closed set is still inadequate in practice; a robust open-set system needs to effectively reject unknown gestures while correctly classifying known ones, which is rarely explored in the field of myoelectric gesture recognition. To handle this challenge, we first report a significant distinction in prediction inconsistency discovered for unknown classes, which arises from different perspectives and can substantially enhance open-set recognition performance. Based on this insight, we propose a novel dual-perspective inconsistency learning approach, PredIN, to explicitly magnify the prediction inconsistency by enhancing the inconsistency of class feature distribution within different perspectives. Specifically, PredIN maximizes the class feature distribution inconsistency among the dual perspectives to enhance their differences. Meanwhile, it optimizes inter-class separability within an individual perspective to maintain individual performance. Comprehensive experiments on various benchmark datasets demonstrate that the PredIN outperforms state-of-the-art methods by a clear margin. Our proposed method simultaneously achieves accurate closed-set classification for predefined gestures and effective rejection for unknown gestures, exhibiting its efficacy and superiority in open-set gesture recognition based on sEMG.