Re: Scrap it
This is actually one of the first case studies you come across in economics.
The basic problem is that farmers have to predict the price of their crops up to a year before they are sold, and once the seeds are or are not sown, they are committed to their decisions. Furthermore, in an imperfect world they don't know what everyone else is doing.
Human nature being what it is, this situation rapidly spirals into a boom/bust cycle, where a glut in a crop pushes prices down, making fewer farmers want/afford to grow next season, resulting in scarcity and high prices (see the current broccoli greens rationing because of Spain's problems), and the high prices prompt investment in the crop and then another glut, and so on. It's also pretty clear that in this process quite a few farmer will take a financial bath on each cycle.
Clearly that's simplistic, but having a guaranteed minimum return on investment via subsidies prevents this cycle taking hold.
Also, as others have said, keeping farms running is of vital strategic importance, not just due to wars etc but due to the ease with which an oil crisis (or French docker's strike) could leave us up sh*t creek.