Researchers have proposed various methods for visually interpreting the Convolutional Neural Network (CNN) via saliency maps, which include Class-Activation-Map (CAM) based approaches as a leading family. However, in terms of the internal design logic, existing CAM-based approaches often overlook the causal perspective that answers the core "why" question to help humans understand the explanation. Additionally, current CNN explanations lack the consideration of both necessity and sufficiency, two complementary sides of a desirable explanation. This paper presents a causality-driven framework, SUNY, designed to rationalize the explanations toward better human understanding. Using the CNN model's input features or internal filters as hypothetical causes, SUNY generates explanations by bi-directional quantifications on both the necessary and sufficient perspectives. Extensive evaluations justify that SUNY not only produces more informative and convincing explanations from the angles of necessity and sufficiency, but also achieves performances competitive to other approaches across different CNN architectures over large-scale datasets, including ILSVRC2012 and CUB-200-2011.