Honestly I think children should be allowed to be occasionally greedy and selfish. I think that it is a normal part of being human and everyone should be allowed some of it. Adults certainly do it. Why do children have to be perfect? But I do draw the line at being rude. So for example for my children we use the phrase, "I'm feeling really attached to this and I don't want to share it." That works for mommy's wedding ring and it works for something that a kid has done alone. You can't do it all the time--we do stress that we are overall a sharing family but that starts way back in how I have treated them. I share almost everything--but my wedding rings.
My kids are only two and four and they have both already made food and been unwilling to share it. I didn't permit them to gorge--I doled it out and it wasn't that fun for them after a while. Usually they relent on their own. I don't feel like possessiveness about food is a good thing to fight them on. I want to save my fights for who they date. :)