In this study, we revisit the fundamental setting of face-swapping models and reveal that only using implicit supervision for training leads to the difficulty of advanced methods to preserve the source identity. We propose a novel reverse pseudo-input generation approach to offer supplemental data for training face-swapping models, which addresses the aforementioned issue. Unlike the traditional pseudo-label-based training strategy, we assume that arbitrary real facial images could serve as the ground-truth outputs for the face-swapping network and try to generate corresponding input < source, target > pair data. Specifically, we involve a source-creating surrogate that alters the attributes of the real image while keeping the identity, and a target-creating surrogate intends to synthesize attribute-preserved target images with different identities. Our framework, which utilizes proxy-paired data as explicit supervision to direct the face-swapping training process, partially fulfills a credible and effective optimization direction to boost the identity-preserving capability. We design explicit and implicit adaption strategies to better approximate the explicit supervision for face swapping. Quantitative and qualitative experiments on FF++, FFHQ, and wild images show that our framework could improve the performance of various face-swapping pipelines in terms of visual fidelity and ID preserving. Furthermore, we display applications with our method on re-aging, swappable attribute customization, cross-domain, and video face swapping. Code is available under https://github.com/ICTMCG/CSCS.