Federated learning (FL) enables multiple participants to train a global machine learning model without sharing their private training data. Peer-to-peer (P2P) FL advances existing centralized FL paradigms by eliminating the server that aggregates local models from participants and then updates the global model. However, P2P FL is vulnerable to (i) honest-but-curious participants whose objective is to infer private training data of other participants, and (ii) Byzantine participants who can transmit arbitrarily manipulated local models to corrupt the learning process. P2P FL schemes that simultaneously guarantee Byzantine resilience and preserve privacy have been less studied. In this paper, we develop Brave, a protocol that ensures Byzantine Resilience And privacy-preserving property for P2P FL in the presence of both types of adversaries. We show that Brave preserves privacy by establishing that any honest-but-curious adversary cannot infer other participants' private data by observing their models. We further prove that Brave is Byzantine-resilient, which guarantees that all benign participants converge to an identical model that deviates from a global model trained without Byzantine adversaries by a bounded distance. We evaluate Brave against three state-of-the-art adversaries on a P2P FL for image classification tasks on benchmark datasets CIFAR10 and MNIST. Our results show that the global model learned with Brave in the presence of adversaries achieves comparable classification accuracy to a global model trained in the absence of any adversary.