Objective. Breast cancer is the major cause of cancer death among women worldwide. Deep learning-based computer-aided diagnosis (CAD) systems for classifying lesions in breast ultrasound images can help materialise the early detection of breast cancer and enhance survival chances. Approach. This paper presents a completely automated BUS diagnosis system with modular convolutional neural networks tuned with novel loss functions. The proposed network comprises a dynamic channel input enhancement network, an attention-guided InceptionV3-based feature extraction network, a classification network, and a parallel feature transformation network to map deep features into quantitative ultrasound (QUS) feature space. These networks function together to improve classification accuracy by increasing the separation of benign and malignant class-specific features and enriching them simultaneously. Unlike the categorical crossentropy (CCE) loss-based traditional approaches, our method uses two additional novel losses: class activation mapping (CAM)-based and QUS feature-based losses, to capacitate the overall network learn the extraction of clinically valued lesion shape and texture-related properties focusing primarily the lesion area for explainable AI (XAI). Main results. Experiments on four public, one private, and a combined breast ultrasound dataset are used to validate our strategy. The suggested technique obtains an accuracy of 97.28%, sensitivity of 93.87%, F1-score of 95.42% on dataset 1 (BUSI), and an accuracy of 91.50%, sensitivity of 89.38%, and F1-score of 89.31% on the combined dataset, consisting of 1494 images collected from hospitals in five demographic locations using four ultrasound systems of different manufacturers. These results outperform techniques reported in the literature by a considerable margin. Significance. The proposed CAD system provides diagnosis from the auto-focused lesion area of B-mode BUS images, avoiding the explicit requirement of any segmentation or region of interest extraction, and thus can be a handy tool for making accurate and reliable diagnoses even in unspecialized healthcare centers.