I am of Chinese descent, though not born or brought up in China.
Yes, I was brought up to understand that it is rude to leave food on your plate. Every morsel of food must be eaten, every grain of rice should be carefully scooped up and finished. Wasting food is the one thing that we can get severely punished for. Anything that I could not finish when I was a child, was finished by my dad. All my Chinese friends in the neighbourhood were brought up the same way.
When visiting, we are to finish our food, and we are not allowed to ask for seconds until all the members of the older generation had finished eating. We were, however, allowed to have seconds if someone from the older generation offers the food to us. It is considered very rude to ask, but not at all rude to accept the offer of more food.