Identification of repeating earthquakes (repeaters) usually depends on waveform similarity expressed as the corresponding cross-correlation coefficient (CC) above a prescribed threshold, typically ranging from 0.70 to 0.98. However, the robustness and effectiveness of such a strategy have never been thoroughly examined. In this study, we examine whether CC is a valid proxy for repeater identification through both synthetic and real earthquake experiments. We reveal that CC is controlled by not only the inter-event distance but also many other factors, including station azimuth, epicentral distance, velocity structure, etc. Consequently, CC lacks the resolution in identifying true repeaters. We propose a physics-based approach that considers both inter-event separation and rupture radius. For an event pair to be true repeaters, their inter-event separation must be smaller than the rupture radius of the larger event. Our results imply that a systematic recheck of previously identified repeaters and associated interpretations/hypotheses may be important and necessary.