Analyzing functional brain networks using functional magnetic resonance imaging (fMRI) is crucial for understanding psychiatric disorders and addictive behaviors. While existing fMRI-based graph convolutional networks (GCNs) show considerable promise for feature extraction, they often fall short in characterizing complex relationships between brain regions and demographic factors and accounting for interpretable variables linked to psychiatric conditions. We propose NeuroTree to overcome these limitations, integrating a k-hop AGE-GCN with neural ordinary differential equations (ODEs). This framework leverages an attention mechanism to optimize functional connectivity (FC), thereby enhancing dynamic FC feature learning for brain disease classification. Furthermore, NeuroTree effectively decodes fMRI network features into tree structures, which improves the capture of high-order brain regional pathway features and enables the identification of hierarchical neural behavioral patterns essential for understanding disease-related brain subnetworks. Our empirical evaluations demonstrate that NeuroTree achieves state-of-the-art performance across two distinct mental disorder datasets and provides valuable insights into age-related deterioration patterns. These findings underscore the model's efficacy in predicting psychiatric disorders and elucidating their underlying neural mechanisms.