Analysis of respiratory sounds is an area where deep neural networks (DNNs) may benefit clinicians and patients for diagnostic purposes due to their classification power. However, explaining the predictions made by DNNs remains a challenge. Currently, most explanation methods focus on post-hoc explanations, where a separate explanatory model is used to explain a trained DNN. Due to the complex nature of respiratory sound classification pipeline involving signal processing such as frequency analysis and wavelet analysis, post-hoc methods cannot uncover the underlying inference process of DNNs, highlighting the importance of designing DNNs with intrinsic interpretability. In this paper, we propose a self-explaining DNN for respiratory sound classification based on prototype learning. Our model explains its behavior by generating sample prototypes while attaching these prototypes to a layer inside the neural network. Furthermore, we design a scale-free interpretability mechanism, in which the model reaches its final decision by dissecting the input and looking for similarities between several parts of the input and the prototypes. The experimental findings on the largest public respiratory sound database demonstrate that our method achieves comparable, sometimes better, performance with the non-interpretable counterparts while offering state-of-the-art interpretability. The code will be released upon acceptance.