The Economist (see also HERE) asks why there is no apparent causal (or even correlative) relationship between education and democracy. They claim, "It is possible, however, that education reinforces authority and the power of ruling elites; indeed, it may often be designed to do precisely this." This seems entirely plausible to me.
A working paper by Bang and Mitra shows that, once we control for certain other factors, the impact of education on growth is even ambiguous. What other factors, you ask? Gender equity/bias. One explanation here is that in countries that have high rates of education among men (but not among women) education is doing precisely what the Economist suggests - fortifying the established position of the traditional elites.