Large language models are rapidly being deployed as AI tutors, yet current evaluation paradigms assess problem-solving accuracy and generic safety in isolation - failing to capture whether a model is simultaneously pedagogically effective and safe across sustained interaction. We argue that tutoring safety is fundamentally different from conventional LLM safety: the primary risk is not toxic content but the quiet erosion of learning through answer over-disclosure, misconception reinforcement, and the abdication of scaffolding. To systematically study this failure mode, we introduce SafeTutors, a benchmark that jointly evaluates safety and pedagogy across mathematics, physics, and chemistry. SafeTutors is organized around a theoretically grounded risk taxonomy comprising 11 harm dimensions and 48 sub-risks drawn from learning-science literature. We uncover that all models show broad harm; scale doesn’t reliably help; and multi-turn dialogue worsens behavior, with pedagogical failures rising from 17.7% to 77.8%. Harms also vary by subject, so mitigations must be discipline-aware, and single-turn “safe/helpful” results can mask systematic tutor failure over extended interaction.