The present paper is a literature and experience summary about contradictions existing in higher education, nowadays. Thus, it is important to understand the underlying reasons and historical background to find ability to move towards higher education system for sustainability. Seven main contradiction groups have been distinguished and an overview is given in the article. The analysis is more focused on a situation in Latvia and the post-soviet space since the authors are well acquainted with the system. The main future research object is university mission, since from the mission statement analysis it has been found that low rated universities lack the distinction between education and training, having bigger stress on training, and that is growing into future problems and this situation interferes with the sustainable education goal.