"Why is the farmer responsible for saving the best seed to improve the next generation instead of a big corporation?"
Simple: Vertical integration. The more I do as the farmer the more money that sticks to my palm rather than getting paid out to "Big Corporations" and out as taxes. Farmers use vertical integration for the exact same reasons Big Corporations use it - we improve our bottom line.
"Why shouldn't farmers best seeds possible"
And there's the quandary. You see the seed that I save and select over the generations is the BEST seed for my growing conditions, soils and management. The seed provided by Big Corp is designed to work with their pesticides and herbicides, their artificial fertilizers and equipment which the farmer must then buy into as well increasing the farmer's costs. Best does not mean the same thing in all situations. My seed stock, be it plant or animal, is far better than Big Corp's, for my situation. This also gives me control over my systems rather than putting me under the thumb of Big Corp.
"We don't expect farmers to build their own tractors"
Funny you should mention that because actually farmers tend to be engineers and inventors, often building machinery and systems for their own use. Farmers tend to be on that leading edge of technology while the big manufacturers like John Deere are producing for the masses. If a machine doesn't do what I need I either modify it or build my own. Standard Operating Procedure on many farms.