Confirming Correct, Missing the Rest: LLM Tutoring Agents Struggle Where Feedback Matters Most

Effective tutoring requires distinguishing optimal (expert-path), valid-alternative (valid but suboptimal), and incorrect student solutions, a distinction central to intelligent tutoring systems (ITS) yet untested for LLM-based tutors. As LLMs are increasingly explored as conversational complements to ITS for scalable feedback, evaluating their diagnostic precision is essential. We benchmark seven LLMs as feedback agents in propositional logic using knowledge-graph-derived ground truth across 10,836 solution-feedback pairs \footnote{\url{https://github.com/anonymouspaper64-debug/anonymous_paper.git}} and three prompt-level feedback conditions. Our analysis show that models achieve near-ceiling performance on optimal steps but systematically over-reject valid-alternative reasoning and over-validate incorrect solutions, precisely where adaptive tutoring matters most. These failure modes persist regardless of solution context or model capability, indicating architectural rather than informational limits. Accurate classification does not reliably translate into pedagogically actionable feedback, exposing a gap between diagnostic judgment and instructional effectiveness. LLMs thus cannot resolve the assistance dilemma without ITS-grounded mechanisms; they are better positioned within hybrid systems that combine LLM flexibility with ITS student modeling.