In the agriculture industry there are subsidies available to farmers to help offset the large costs associated with producing produce and livestock. These subsidies result in lower prices for consumers in the market. Would you consider education to be similar in nature to this concept of subsidies in agriculture?
Although you could argue that these are similar, I would argue that they are fundamentally different. The reason for this is that education has many more positive externalities than agriculture does. This means that it makes sense for a government to promote education while it is more sensible for a government to allow agriculture to be driven by market forces.
Externalities are impacts from a given activity that are felt by people who are not involved in the activity. These externalities can be negative or they can be positive. Governments should try to intervene to prevent negative externalities and promote things that provide positive externalities.
Agriculture creates relatively few positive externalities. This is not to say that agriculture is bad. What it means is that agriculture does not do much to help people other than the people who are involved in producing, selling, and buying agricultural products.
By contrast, many people benefit from education even if they are not involved in it. If I am not a teacher or a student, and if I do not have kids in school, I can still benefit from public education. I gain, for example, because the people who get good educations can become economically productive and can help our society. Because education provides positive externalities and agriculture largely does not, there is a major difference between subsidizing agriculture and providing public education.