It was a dish concocted to con the emperors. The imperial livestock farm could rear very good quality duck of course. Emperors' meals were lavishly wasteful with 64-dish standard, of which they just ate a little of each dish. The cooks realised the duck meat was delicious and nutricious, and kept it for themselves and to bribe the eunuchs, served only the skin to the emperors with some sweet sauce and paper-thin bun. There were so many dishes that the emperors didn't bother to notice and the skin was actually quite good anyway.
Foreign tourists, diplomats and dignitaries thereafter are being conned the same way until it attained international status symbol when peasants with some money start conning themselves too, much to the delight of duck merchants and restauranteurs. Eat skin? What the hell is that logic? Even an idiot knows how to spit out skin and eat meat.