If the
signalling model of education is at all accurate, then it's possible that at least some types of education can have
negative externalities.
Imagine the (highly unlikely) world where college education provides nothing of value, but serves as a way for employers to distinguish between the (probably) smart and hard-working and those who (probably) are not. Then college graduates will earn more than non-graduates because of this and cohort effects, not because college teaches them anything. Now, suppose you introduce subsidies for college. Since the credibility of a signal depends on its cost, this just means that students have to spend more time and money on education to get the same signal. In that case, subsidies are
completely wasteful. Signalling almost certainly isn't the entire reason for college, but to the degree it is relevant it reduces the social benefit of incentivising people to go there.