I believe that children should be taught from an early age to only take what they think they can handle, so that they don't waste food, or anything else, because children are extremely lucky if they can get food when they want it. Therefore, they should be shown that they shouldn't waste any of it by taking more than they can handle. Now, my debate would be different if the child is honestly full. But many times, they do it to go play, or because they don't want to eat anymore, and this way they will learn not to take more than they think they can handle.
I don't think parents should nag their kids about eating everything on their plate, but let them choose how much they want on their plate. If they choose what and how much they want so that the child won't overfeed themselves too often. We all can admit that there are too many people on this planet and that food will eventually become scarce. The soil on which we are farming from will eventually not have any nutrients. The animals that we slaughter for meat will eventually become so rare, that we will make them extinct for the meat. I can assure you that there will probably be a war over food in the future. Why waste food? Even now there are a ton of starving kids in third world countries in Africa and South America.
Teaching them to put less on their plates and having them eat everything are not mutually exclusive. If they know that the consequences of putting more on their plate than they need is that they'll have to eat more than desired, they will be deterred from doing this again. In Chinese culture, we are taught from an early age (well, I'm taught anyway, I know a lot of families, regrettably, don't do it any more) that every last grain of rice comes from the sweat of farmers and that we must not waste it. It is this respect for farmers that has to be cultivated (no pun intended) in children by teaching them to eat everthing.
Instead of forcing them to eat everything, teach them not to suck at choosing appropriate portion sizes for themselves. I can see how this rule would apply back before refrigerators, tupperware, and aluminum foil were invented, but now that those things exist, it's better just to store it and have them eat it later when they're hungry again.
I also don't think forcing kids to eat food they don't like is a crappy thing to do. All my life I've hated cooked carrots, and that was one of the things that always seemed to end up being put on my plate (I didn't get to pick). I refused to eat them and was punished for it. The way I see it now that I think about it, I was actually being punished for having different taste buds. If they really wanted me to eat carrots, they could have not cooked one and I would have eaten it without a problem. I wish I would have thought of that when I was a kid.
I don't make my son eat anything he doesn't like, I talk him into trying it at least once, but if he doesn't like it I'll go that little bit extra out of my way to make sure I get things he does like. And that's not being some "liberal sissy parent who let's his kid walk all over him", that's being a dad who gives a sh*t and doesn't want his kid puking all over my house.
Oddly enough, at 16, his favorite vegetables are brussel sprouts and asparagus, and it's probably because I didn't force him to eat the crap when he was 6. Taste buds mature. I might even like cooked carrots at this point, but I'm sure as hell not willing to find out. I've gone 17 years without eating them now, and I'm not dead, so screw cooked carrots.
The problem is usually not that kids out too much on their plates, but that parents make their plates for them and expect them to eat everything. This happens especially in certain cultures, and usually with children that are on the thinner or smaller size range for their age, especially boys. But it is abusive to force them to eat beyond feeling full because it can make them physically sick and anxious about eating, which can lead to eating disorders. Parents should teach their children good eating habits from an early age, which includes sensing how much food you need and not eating beyond that point. Also, even now as an adult, sometimes i take more food than i need and only realize halfway through the meal, i dont "punish" myself by making myself finish. I try to learn from my mistake.
If a child is hungry, they will eat. They should be taught to put less on their plate instead and they will also be taught not to be wasteful. Teaching a child to eat everything on their plate is borderline abuse and is probably a cause for the obesity problem in the world. When your child is full, that's a bad thing. That means they ate too much and their body will store the extra food in fat cells. Don't teach your child gluttony.
Eating past being full is unhealthy and wasteful. Leftovers should be saved for later, and children should practice healthy eating habits to prevent future ailments, such as obesity.
If people are uncomfortable throwing food out that they for some reason can not save, they should understand that eating it doesn't make it any less gone or in the stomach of someone who needs it. Just don't prepare more food than typically necessary.