This article interrogates a key feature of anarchist education; focusing on a problem with implications not only for anarchist conceptions of education, but for anarchist philosophy and practice more broadly. The problem is this: if anarchism consists in the principled opposition to all forms of coercive authority, then how is this to be reconciled with situations where justice demands the use of coercion in order to protect some particular good? It seems that anarchist educators are forced to deny coercive authority in principle, whilst at the same time affirming it in practice. This is the paradox of pedagogical authority in anarchist education. Coercive authority is simultaneously impossible and indispensable. Exploring this paradox through a reading of Jacques Derrida's later work, and, in particular, his conception of justice as requiring openness to the singular situation, I argue that in exercising their authority anarchist educators encounter the aporetic moment in anarchism, experiencing what Derrida calls 'the ordeal of the undecidable'. Understood this way, the paradox becomes less an indication of anarchism's limitations than it does its value. For it is here that the problem of pedagogical authority is treated with the gravity that all questions of justice deserve.