If food really is something important for the country, would it not make more sense for the country to prioritize and fund it as opposed to leaving it to the whims of whomever feels like funding it that day?
Most of the benefit of food is private: when I eat, I am no longer hungry. That means I take care of my food myself.
Most of the benefit to education is, as well, private. If I become a lawyer, I capture most of the benefit.
It's when the benefit cannot be internalized that you need government involved. A public good is one that is non-excludable and non-rivalrous. National defense and most environmental causes are examples there. Education is a private good, since it is both trivially excludable as well as (if you listen to any NEA paper about student-teacher ratios) rather rivalrous.