This paper disentangles the role of parents' aspirations against labor market returns in explaining educational choices. We use a static equilibrium unemployment search model with endogenous education. The schooling cost is conditional on parents' education and imperfectly observable, whereas parents (optimally) transmit a taste for work. Intergenerational social mobility is driven by labor market institutions, which shape schooling incentives and parents' aspirations. The latter are defined by a taste for work which increases the utility derived from the revenue of work. We can also see aspirations as a way to insure against unemployment. Indeed, the lower they are, the higher is the utility derived from unemployment income. Therefore, decreasing social inequality should not come from decreasing unemployment income. Indeed, when we decrease it by 20% we observe no change in terms of labor inequality: wage and unemployment disparities are slightly the same. On the other hand, by an insurance behavior, individuals decide to give to their children a lower taste for work in order to limit their frustration in case of unemployment. As a consequence, the average level of education in the population decreases.