Most of farm subsidies that people talk about goes towards food stamp-type programs. Not wanting the poor to starve may be a good reason.

And when people talk about product subsidies (like corn subsidies) they are referring to the insurance system operated by the government. Due to the nature of what is being insured (i.e. something that is likely to affect most policy holders when disaster strikes), it is difficult for private business to provide the necessary insurance.

Traditional insurance products rely on only a few policy holders needing insurance each year. When mass disaster strikes, such as a hurricane destroying homes across a wide area, the government typically does step in to cover the difference. Since this is the norm for agriculture, the government stays at the ready. Farmers still have to maintain a paid policy to be participants in the insurance system.

Perhaps insurance should be abandoned, but it's generally considered a social good.