This study exposes the opinions of a group of former directors of public schools in Chile who were selected by the system of high public management, and who had to leave their posts before the end of their appointment period. The responses evidence the fragility of the local organization of public education, in terms of the interference of the local political authority in the early dismissal of school leaders and identify the various pressures the leaders received from the higher authorities in the exercise of their position. The main problems they faced were the lack of support during the installation phases as well as a lack of monitoring and evaluation of their performance, which are widespread among Latin American countries, given the trends. This paper examines the selection process for High Public Management, the background on the subject, the answers of the interviewees, and an analysis of the interviews. It concludes with some proposals to improve the selection system.