Text Style Transfer (TST) aims to rewrite text in a target style while preserving its semantics. However, existing methods rely on style-specific supervision and implicit generation, leading to poor generalization and semantic degradation given the inherent scarcity of parallel data. We propose Style-Generalizable Trajectory Reasoning (SGTR), a novel framework that formulates TST as the joint modeling of reasoning trajectories and outputs, decomposing the process into three interpretable stages: style understanding, deviation localization, and reflection refinement. To further enhance stylistic generalization, we introduce a latent contrastive learning objective, enabling the model to disentangle stylistic attributes from semantic content directly within its hidden representations. We distill these sophisticated analytical capabilities into a lightweight student model. Experiments demonstrate that SGTR consistently outperforms strong baselines in both style quality and semantic preservation, while exhibiting superior zero-shot generalization to unseen styles.