Biometric systems based on electroencephalography (EEG) are increasingly used for user authentication due to the uniqueness and difficulty in replicating brain signals. However, current systems, particularly those relying on subsymbolic one-class neural networks, face challenges in explainability and robustness against noisy or synthetic inputs. In this work, we introduce a hybrid subsymbolic and symbolic pipeline for an explainable EEG authentication system. The system first applies a symbolic coherence-checking module to evaluate signal quality, using neurophysiological criteria such as interchannel consistency and temporal stability. Inputs failing this stage, often corresponding to noisy or improperly measured signals, are immediately rejected. High-coherence signals are then processed in parallel by two components: a one-class neural network trained on legitimate user data, and a symbolic module based on Inductive Logic Programming (ILP). The symbolic module derives and applies logic rules grounded in EEG feature distributions of the honest user, offering transparent justifications for acceptance or rejection decisions. In cases of disagreement between modules, the system combines their outputs through a weighted decision strategy. This approach enhances security against adversarial input and resilience to noisy measurements, and is enriched by symbolic logs for explainability, which promotes interpretability, defining a way for trustworthy EEG-based authentication in practical deployments.