Teacher rationales can help a smaller model answer health professions questions, but they can also reinforce errors. We examined when they help and how this evidence can guide training using Brazilian Portuguese questions from medical and multiprofessional residency examinations. First, we measured how a teacher rationale changed the student's probability of selecting the correct answer and compared this effect with rationales drawn from other questions. The complete rationale increased this probability by 21~p.p. when the teacher was correct and decreased it by 14~p.p. when the teacher was wrong. By intervening on the reasoning content, we showed that shuffled rationales did not produce the same pattern. Guided by this result, we trained only with rationales attached to correct teacher answers and compared answer-only training, step-by-step distillation, and our proposed Distill-SFT method. Distill-SFT showed a modest advantage over step-by-step distillation on previously missed questions under reasoning, while using fewer training instances by combining the answer and rationale into a single target. We also investigated catastrophic forgetting using the out-of-domain ENEM dataset. Answer-only training reduced reasoning accuracy by 12~p.p. relative to baseline, compared with approximately 4~p.p. for either rationale-based training method. Together, these findings support a workflow that audits rationale content before distillation, verifies teacher answers before supervision, and trains compact models efficiently for health professions question answering.

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