ABSTRACT The inclusive education policy agenda has not made a significant impact on the global problem of educational exclusion. Explanations for this lack of impact include inadequate teacher education, lack of resources, negative attitudes, and a policy-practice gap. This paper takes a different turn and, using the concept of classification, argues that the challenge to achieve more inclusive education is more fundamental than has been previously articulated. Key tenets of the inclusive education agenda demand a weakening of the insulation between categories that are sustained and advanced by current marketised and standards-driven education systems. Inclusive schooling weakens spatial insulation, collaboration weakens professional insulation, transformability weakens ability insulation, intersectionality weakens identity insulation, and inclusive pedagogy weakens pedagogical insulation. When inclusive education is mapped onto strongly classified education systems, limited instantiations of inclusive education are inevitable, and difference and exclusion are re-inscribed. Change is possible if 1. Those advancing the inclusive education agenda acknowledge the identities and defences that classification constructs. 2. The workings of power that sustain insulation between categories in education are identified. 3. Counter-hegemonic action that weakens insulation and blurs boundaries is encouraged.