Conversational AI is increasingly used for advice, interpretation, reassurance, and decision support in contexts where users may be vulnerable, uncertain, or dependent on the system's apparent competence. Existing alignment work often focuses on model objectives, preference optimization, or output correctness. Yet, many harms arise through interaction: how systems frame authority, express uncertainty, simulate empathy, support reasoning, and make boundaries legible. This paper introduces the Layered Cognitive Alignment Model (LCAM), a conceptual and normative framework for diagnosing interac-tional alignment failures in conversational AI. LCAM defines alignment as a calibrated fit among system behavior, user goals, task demands, and normative context. It distinguishes five layers of fit: perceptual, semantic, affective, cognitive, and ethical, and two diagnostic polarities of misalignment: underfit and overreach. We apply LCAM to a published LLM counseling example, showing how an apparently supportive response can reinforce harmful beliefs, simulate inappropriate care, and obscure role boundaries. By translating conversational failures into audit and governance questions concerning over-reliance, false intimacy, autonomy erosion, boundary confusion, and inappropriate trust, LCAM offers a theoretical and normative lens for evaluating conversational AI beyond accuracy, helpfulness, or trust.