In this study, a novel computer aided diagnosis (CADx) framework is devised to investigate interpretability for classifying breast masses. Recently, a deep learning technology has been successfully applied to medical image analysis including CADx. Existing deep learning based CADx approaches, however, have a limitation in explaining the diagnostic decision. In real clinical practice, clinical decisions could be made with reasonable explanation. So current deep learning approaches in CADx are limited in real world deployment. In this paper, we investigate interpretability in CADx with the proposed interpretable CADx (ICADx) framework. The proposed framework is devised with a generative adversarial network, which consists of interpretable diagnosis network and synthetic lesion generative network to learn the relationship between malignancy and a standardized description (BI-RADS). The lesion generative network and the interpretable diagnosis network compete in an adversarial learning so that the two networks are improved. The effectiveness of the proposed method was validated on public mammogram database. Experimental results showed that the proposed ICADx framework could provide the interpretability of mass as well as mass classification. It was mainly attributed to the fact that the proposed method was effectively trained to find the relationship between malignancy and interpretations via the adversarial learning. These results imply that the proposed ICADx framework could be a promising approach to develop the CADx system.