Supervised fine-tuning with synthetic rationales is widely assumed to improve clinical prediction by teaching models not only what to predict but why. We test this assumption on five-year Alzheimer's disease and related dementias (ADRD) prediction from longitudinal health histories. In this setting, we generate training rationales using the correct labels, then fine-tune models to output a rationale followed by a label. Across a large-scale controlled experiment of 504 configurations, we find that Rationale First SFT consistently and substantially hurts predictive performance relative to Label Only fine-tuning. The degradation persists across model families and data scales, and is not resolved by using a reasoning-oriented base model. A fixed-protocol cardiovascular disease (CVD) validation reproduces similar findings. Crucially, the failure is not explained by poor rationale quality: human expert annotation confirms that the generated rationales are medically accurate and faithfully grounded in patient-specific evidence, and few-shot experiments show that the same rationales improve performance when used as inference-time demonstrations rather than training targets. A simple label-ordering intervention clarifies the mechanism: placing the prediction before the same rationale restores predictive performance. This suggests that conditioning predictions on generated rationales contributes to the degradation. We hope our work paves the way toward a more precise understanding of when and how rationale-based supervision helps and when it does not, guiding the responsible development of language models for high-stakes clinical prediction.

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