Critical peace education literature has focused attention on how programmes that promise to teach peace contribute to and contest existing power relations. However, using social theory to work out the relationship between peace education programmes and their context is only beginning. This paper uses a document review and interviews with experts to examine the expectations for peace education in Colombia and the challenges these programmes face. It finds there is a coherent set of demands that constitute peace education, which primarily focus on developing empathy and critical thinking. These aims face material restrictions of a lack of time and space in the curriculum, but also the problem of embedded competitive behaviour between pupils. Bourdieu's toolkit of habitus, field and capital frames this obstacle as part of the struggle to determine what constitutes legitimate capital within a field. This framing has two benefits. It prevents the problem of competitive inter-pupil relations being located within the actions of individual teachers and students. It also allows for solutions that address the structural challenges facing peace education. This use of Bourdieu focuses attention on the systemic obstacles facing peace education and so helps move the literature away from problem-solving and individualised analysis.