Automated interpretation and reporting of chest X-rays (CXRs) hold significant promise in reducing diagnostic errors and supporting radiologists under heavy clinical workloads. However, existing methods typically rely on global visual features and token-level supervision, limiting their sensitivity to subtle abnormalities and reducing their clinical reliability. To address these challenges, we present Reflective X-ray Network (RefleXNet), which systematically integrates multi-scale visual feature fusion and anatomical relational reasoning with a targeted self-reflective learning strategy. RefleXNet first constructs multi-scale visual representations and captures anatomical context through graph-based relational modeling. Building upon these representations, we introduce a targeted self-reflection strategy that uses clinically guided feedback from generated reports to selectively refine abnormality predictions and their associated region-level visual features. Extensive experiments on MIMIC-CXR demonstrate that RefleXNet consistently outperforms state-of-the-art baselines across clinical factual correctness metrics. Notably, our compact 3B-parameter model surpasses several recent models with over twice the parameter count. Additionally, RefleXNet exhibits strong generalization performance in zero-shot evaluations on IU-Xray compared with leading multimodal language models, highlighting its robustness and clinical effectiveness.