Convolutional neural network based systems have largely failed to be adopted in many high-risk application areas, including healthcare, military, security, transportation, finance, and legal, due to their highly uninterpretable “black-box” nature. Towards solving this deficiency, we teach a novel multi-task capsule network to improve the explainability of predictions by embodying the same high-level language used by human-experts. Our explainable capsule network, X-Caps, encodes high-level visual object attributes within the vectors of its capsules, then forms predictions based solely on these human-interpretable features. To encode attributes, X-Caps utilizes a new routing sigmoid function to independently route information from child capsules to parents. Further, to provide radiologists with an estimate of model confidence, we train our network on a distribution of expert labels, modeling inter-observer agreement and punishing over/under confidence during training, supervised by human-experts’ agreement. X-Caps simultaneously learns attribute and malignancy scores from a multi-center dataset of over 1000 CT scans of lung cancer screening patients. We demonstrate a simple 2D capsule network can outperform a state-of-the-art deep dense dual-path 3D CNN at capturing visually-interpretable high-level attributes and malignancy prediction, while providing malignancy prediction scores approaching that of non-explainable 3D CNNs. To the best of our knowledge, this is the first study to investigate capsule networks for making predictions based on radiologist-level interpretable attributes and its applications to medical image diagnosis. Code is publicly available at https://github.com/lalonderodney/X-Caps.