Imitation learning allows social robots to learn new skills from human teachers without substantial manual programming, but it is difficult for robotic imitation learning systems to generalize demonstrated skills as well as human learners do. Contemporary neurocomputational approaches to imitation learning achieve limited generalization at the cost of data-intensive training, and often produce opaque models that are difficult to understand and debug. In this study, we explore the viability of developing purely-neural controllers for social robots that learn to imitate by reasoning about the underlying intentions of demonstrated behaviors. We present NeuroCERIL, a brain-inspired neurocognitive architecture that uses a novel hypothetico-deductive reasoning procedure to produce generalizable and human-readable explanations for demonstrated behavior. This approach combines bottom-up abductive inference with top-down predictive verification, and captures important aspects of human causal reasoning that are relevant to a broad range of cognitive domains. Our empirical results demonstrate that NeuroCERIL can learn various procedural skills in a simulated robotic imitation learning domain. We also show that its causal reasoning procedure is computationally efficient, and that its memory use is dominated by highly transient short-term memories, much like human working memory. We conclude that NeuroCERIL is a viable neural model of human-like imitation learning that can improve human-robot collaboration and contribute to investigations of the neurocomputational basis of human cognition.