Graph Neural Networks (GNNs) have achieved impressive performance in semi-supervised graph anomaly detection (GAD). While many GNN variants have been developed for this task, they largely focus on advanced message aggregation schemes, leaving the message routing aspect underexplored. We argue that the commonly used broadcast-based routing can also hinder generalization, particularly in the presence of rare and structurally challenging (vertices with a high-degree) anomalies. To address this, we propose Binary Message Passing (BMP), a novel routing paradigm that models the message flow of each vertex as a binary tree (BMP tree), where vanilla graph convolution is decoupled by its left and right subtrees. Each vertex recursively gathers information from neighbors with higher anomaly probabilities within each subtree, thereby amplifying the propagation of anomaly information across the topology. The anomaly probabilities are estimated and updated by the model itself, enabling adaptive, self-supervised routing over iterations. Furthermore, combining multiple BMP trees into a BMP forest provides multi-scale structural context, enhancing the expressiveness of final vertex embeddings. Extensive experiments show that BMP improves detection performance under limited supervision while exhibiting better generalization across structurally diverse anomalies.