Medical image labels are often organized by taxonomies (e.g., organ - tissue - subtype), yet standard self-supervised learning (SSL) ignores this structure. We present a hierarchy-preserving contrastive framework that makes the label tree a first-class training signal and an evaluation target. Our approach introduces two plug-in objectives: Hierarchy-Weighted Contrastive (HWC), which scales positive/negative pair strengths by shared ancestors to promote within-parent coherence, and Level-Aware Margin (LAM), a prototype margin that separates ancestor groups across levels. The formulation is geometry-agnostic and applies to Euclidean and hyperbolic embeddings without architectural changes. Across several benchmarks, including breast histopathology, the proposed objectives consistently improve representation quality over strong SSL baselines while better respecting the taxonomy. We evaluate with metrics tailored to hierarchy faithfulness: HF1 (hierarchical F1), H-Acc (tree-distance-weighted accuracy), and parent-distance violation rate. We also report top-1 accuracy for completeness. Ablations show that HWC and LAM are effective even without curvature, and combining them yields the most taxonomy-aligned representations. Taken together, these results provide a simple, general recipe for learning medical image representations that respect the label tree and advance both performance and interpretability in hierarchy-rich domains.