In light of the Danish government's goal of 95% of every cohort achieving higher education by 2015, we investigate educational mobility in Denmark. Following 800,000 Danes and their parents, we found that children of parents with only basic education had a three-times-higher risk of achieving only basic education, compared with the children of well-educated parents. These social differences in educational achievements were found despite free education and generous governmental grants and loans. We found general upgrading of a population's educational level to be a tardy process which implies breaking the bonds of negative social inheritance to increase intergenerational social mobility in the society; thus, the government's 95% goal is unlikely to be achieved by 2015.