The Concept Bottleneck Model (CBM) is an interpretable neural network that leverages high-level concepts to explain model decisions and conduct human-machine interaction. However, in real-world scenarios, the deficiency of informative concepts can impede the model's interpretability and subsequent interventions. This paper proves that insufficient concept information can lead to an inherent dilemma of concept and label distortions in CBM. To address this challenge, we propose the Decoupling Concept Bottleneck Model (DCBM), which comprises two phases: 1) DCBM for prediction and interpretation, which decouples heterogeneous information into explicit and implicit concepts while maintaining high label and concept accuracy, and 2) DCBM for human-machine interaction, which automatically corrects labels and traces wrong concepts via mutual information estimation. The construction of the interaction system can be formulated as a light min-max optimization problem. Extensive experiments expose the success of alleviating concept/label distortions, especially when concepts are insufficient. In particular, we propose the Concept Contribution Score (CCS) to quantify the interpretability of DCBM. Numerical results demonstrate that CCS can be guaranteed by the Jensen-Shannon divergence constraint in DCBM. Moreover, DCBM expresses two effective human-machine interactions, including forward intervention and backward rectification, to further promote concept/label accuracy via interaction with human experts.