An electroencephalogram (EEG)-based brain-computer interface (BCI) enables direct communication between the brain and external devices. However, such systems face at least three major challenges in real-world applications: limited decoding accuracy, poor robustness, and privacy risks. Although prior studies have addressed one or two of these issues, methods that simultaneously improve accuracy, robustness, and privacy remain largely unexplored. In this paper, we propose Privacy-preserving Adversarial Transfer (PAT), a unified training framework that combines data alignment, adversarial training, and privacy-preserving transfer. PAT provides a single pipeline that can be instantiated under three privacy-preserving scenarios, i.e., centralized source-free transfer, federated source-free transfer, and transfer with privacy-preserved source data, while jointly improving accuracy and robustness. Experiments on five public EEG datasets under three privacy-preserving scenarios (centralized source-free transfer, federated source-free transfer, and transfer with privacy-preserved source data) show that PAT outperforms over ten classic and state-of-the-art methods in both accuracy and robustness. PAT also outperformed leading transfer learning approaches that do not incorporate any privacy mechanisms by 9.76% in terms of average accuracy and robustness. To our knowledge, this is the first approach that simultaneously addresses all three major challenges in EEG-based BCIs. We believe this work can help motivate further research on more accurate, robust, and privacy-preserving EEG decoding.