This paper investigates and compares the policy trajectories of two halted privatisation reforms -- autonomous private high schools in South Korea (2002-2019) and converted schools in China (1992-2008). The two reforms, ambitiously announced, were put under scrutiny and ultimately halted, when the public discontent about education inequalities was widely expressed. We particularly focus on the profound entanglement between neoliberal forces and contextual specificities, and their conjoint influences on the two reforms. The non-linear trajectories are explained through their reified embrace of neoliberal discourses and strategies, deep-rooted ideologies, political systems, and legitimisation derived from the shared Confucian ideals of 'benevolent governance' and social stability. This paper argues that, in these contexts, the verb form 'neoliberalising' better captures the dynamics and openness of privatisation reforms and renders nuanced understandings beyond the currently dominant neoliberal frames of reference.