Breast cancer is considered the most critical and frequently diagnosed cancer in women worldwide, leading to an increase in cancer-related mortality. Early and accurate detection is crucial as it can help mitigate possible threats while improving survival rates. In terms of prediction, conventional diagnostic methods are often limited by variability, cost, and, most importantly, risk of misdiagnosis. To address these challenges, machine learning (ML) has emerged as a powerful tool for computer-aided diagnosis, with feature selection playing a vital role in improving model performance and interpretability. This research study proposes an integrated framework that incorporates customized Particle Swarm Optimization (PSO) for feature selection. This framework has been evaluated on a comprehensive set of 29 different models, spanning classical classifiers, ensemble techniques, neural networks, probabilistic algorithms, and instance-based algorithms. To ensure interpretability and clinical relevance, the study uses cross-validation in conjunction with explainable AI methods. Experimental evaluation showed that the proposed approach achieved a superior score of 99.1\% across all performance metrics, including accuracy and precision, while effectively reducing dimensionality and providing transparent, model-agnostic explanations. The results highlight the potential of combining swarm intelligence with explainable ML for robust, trustworthy, and clinically meaningful breast cancer diagnosis.