The second lesson I ever learned from origami was that all must be accounted for.
In painting, pottery, sculpting or welding the artist starts with nothing and then adds material. They continue to add material until the project is finished. One way to know the project is complete is to see if any more needs to be added. When the artist can no longer add, the work is finished. This is an additive process.
In woodcarving, stone carving, bonsai, and similar works, the artist starts with too much material. They cut, trim, chisel off excess material so that what remains is beautiful. They continue pulling away the extra until there is nothing worth removing. When the remaining material must stay, that is when the project is complete. This is a subtractive process.
There are also those who combine an additive and subtractive process. Sculpture often uses both, carving away at one material, then attaching a new and different material. But origami is one of the few art forms which avoids addition or subtraction. Certainly, some designs are modular, several sheets added together, but the classic examples tend to be of one sheet. The exact same amount of material is present at the beginning and at the end, without significantly changing the underlying structure of the paper! It is metamorphic in that a sheet can become an elephant, yet subtle in that the sheet is still a sheet.
This is such a powerful lesson because it addresses the need to pay attention to the whole. Nothing is ever created or destroyed, it is only found or hidden, both in reality and in origami. Just because you throw it in the trash does not mean it is gone. Just because you need something doesn't mean it will be supplied. Origami hones the attitude that the artist must take what is there and use all of it as it is.