Integrating Artificial Intelligence (AI) into healthcare has shown tremendous promise in several domains, such as prediction, decision-making, and diagnosis. Nevertheless, the widespread belief that AI is incomprehensible and mysterious has restricted its practical use, particularly in medicine. This skepticism highlights the need for methods that provide precise predictions and clear explanations for these projections. The present study presents a hybrid method “BC2” (Breast Cancer Classification) that combines deep learning techniques to accurately detect breast cancer and provide detailed explanations for its predictions. “BC2” exploits the collaborative effects of Convolutional Neural Networks (CNN) and the Light Gradient Boosting Model (LGBM). The automated feature learning process of the model is integrated into many convolutional layers, and LGBM then follows it to provide predictions for class labels. To evaluate the effectiveness of the proposed approach, the authors performed experiments with real-world Breast Cancer Data. The results demonstrate substantial enhancements compared to the current methods in key metrics such as accuracy, precision, recall, and F1 score. The proposed technique obtains an accuracy of 0.982906, a precision of 0.987179, a recall of 0.987179, and an F1-score of 0.987179, demonstrating its exceptional performance. After generating exact forecasts, authors use the “SHAP” (SHapley Additive exPlanation) approach at local and global levels to explain the reasoning behind each projection. This guarantees clarity and improves the comprehensibility of the predictions made by the proposed model. The proposed hybrid model consists of three main components: a feature learning module, a diagnostic module, and an explanation-generating module. The proposed model can improve medical professionals’ diagnostic skills in managing breast cancer patients by clearly explaining its forecasts.