Panchromatic (PAN) and multi-spectral (MS) image fusion, named Pan-sharpening, refers to super-resolve the low-resolution (LR) multi-spectral (MS) images in the spatial domain to generate the expected high-resolution (HR) MS images, conditioning on the corresponding high-resolution PAN images. In this paper, we present a simple yet effective alternating reverse filtering network for pan-sharpening. Inspired by the classical reverse filtering that reverses images to the status before filtering, we formulate pan-sharpening as an alternately iterative reverse filtering process, which fuses LR MS and HR MS in an interpretable manner. Different from existing model-driven methods that require well-designed priors and degradation assumptions, the reverse filtering process avoids the dependency on pre-defined exact priors. To guarantee the stability and convergence of the iterative process via contraction mapping on a metric space, we develop the learnable multi-scale Gaussian kernel module, instead of using specific filters. We demonstrate the theoretical feasibility of such formulations. Extensive experiments on diverse scenes to thoroughly verify the performance of our method, significantly outperforming the state of the arts.