Debates about artificial intelligence (AI) in education often portray teaching as a modular and procedural job that can increasingly be automated or delegated to technology. This brief communication paper argues that such claims depend on treating teaching as more separable than it is in practice. Drawing on recent literature and empirical studies of large language models and retrieval-augmented generation systems, I argue that although AI can support some bounded functions, instructional work remains difficult to automate in meaningful ways because it is inherently interpretive, relational, and grounded in professional judgment. More fundamentally, teaching and learning are shaped by human cognition, behavior, motivation, and social interaction in ways that cannot be fully specified, predicted, or exhaustively modeled. Tasks that may appear separable in principle derive their instructional value in practice from ongoing contextual interpretation across learners, situations, and relationships. As long as educational practice relies on emergent understanding of human cognition and learning, teaching remains a form of professional work that resists automation. AI may improve access to information and support selected instructional activities, but it does not remove the need for human judgment and relational accountability that effective teaching requires.