Differentiating the intrinsic subtypes of breast cancer is crucial for deciding the best treatment strategy. Deep learning can predict the subtypes from genetic information more accurately than conventional statistical methods, but to date, deep learning has not been directly utilized to examine which genes are associated with which subtypes. To clarify the mechanisms embedded in the intrinsic subtypes, we developed an explainable deep learning model called a point-wise linear (PWL) model that generates a custom-made logistic regression for each patient. Logistic regression, which is familiar to both physicians and medical informatics researchers, allows us to analyze the importance of the feature variables, and the PWL model harnesses these practical abilities of logistic regression. In this study, we show that analyzing breast cancer subtypes is clinically beneficial for patients and one of the best ways to validate the capability of the PWL model. First, we trained the PWL model with RNA-seq data to predict PAM50 intrinsic subtypes and applied it to the 41/50 genes of PAM50 through the subtype prediction task. Second, we developed a deep enrichment analysis method to reveal the relationships between the PAM50 subtypes and the copy numbers of breast cancer. Our findings showed that the PWL model utilized genes relevant to the cell cycle-related pathways. These preliminary successes in breast cancer subtype analysis demonstrate the potential of our analysis strategy to clarify the mechanisms underlying breast cancer and improve overall clinical outcomes.