The reason why it's illegal for farmers to keep seeds is due to patent protection, contractual agreements, intellectual property rights and commercial vs private use.
It's not really universally illegal for farmers to actually keep seeds, but it is prohibited for specific patented varieties, which includes many genetically modified seeds and hybrid seeds.
This is due to companies owning patents on the seeds, and saving, replanting or selling the patented seeds is considered to be infringement, although the Plant Variety Protection Act, allows for farmers to save seeds from any PVPA protected crops for their own use, but not for selling or transferring the seeds.
Following a U.S. Supreme Court Ruling in 1980, living organisms and their genetic material can be patented, which makes it illegal to save and reuse the seeds for the patented plants without permission for doing so.
And farmers also often sign contracts with seed companies which prohibit the farmers from saving and replanting any patented seeds.
And if the farmer were to violate the contracts, it can result in legal action being taken against the farmers.
And patents also are a form of intellectual property that also protects the work of the companies and plant breeders and the purpose is to prevent others from copying and benefiting from their innovations.
Also the prohibition and saving of the seeds and planting also mainly affects commercial farmers that grow patented crops for sale.
Home gardeners can often save the seeds without any legal issues, although commercial farmers have to follow the specific laws and agreements.
The PVPA or Plant Variety Protection Act, also allows farmers to save the seeds from the protected varieties for their own use on their own property.
Although they are not allowed to trade, sell or transfer the seeds to other farmers for planting the seeds.
The laws against saving seeds don't apply to seeds that are not patented.
If the seeds are not patented, then the farmers can save the non patented seeds.