I recently saw the fourth movie with them, Shrek Forever After. The movie hinges on two decisions made in order to make problems disappear. The two problems are worded slightly differently, but in both cases the perennial trickster Rumplestiltskin fulfills them by making the people themselves disappear, cease to exist.
There are a few different ways to interpret this. One is the importance of each individual, our inter-connectedness and interdependence. The other is the wrongness of solving problems by "disappearing" them. I am reminded of the discussion at the end of "Brave New World":
In my mind, this speaks also to the modern idea of "abolishing" genetic disorders such as Down syndrome by prenatal diagnosis and abortion. Can we do it? Yes. If done early enough in the pregnancy, all but the most die-hard right-to-lifers would accept that it is the mother's prerogative to decide whether or not to continue the pregnancy at that point, for whatever reason. But the long-term consequence of the sum of these decisions would be to leave our society without the rich diversity of individuals, as well as to deprive our families and communities of the growth opportunity inherent in learning to accept and celebrate these differences. In the context of Brave New World, we are neither willing to "suffer" the disabilities by learning to accept people with disabilities as they are, nor to "oppose" them by seeking new medical treatments and educational methods to improve their outcomes. Instead, we just make the individuals themselves disappear -- cease to exist.
Ironically, even as we embark on informal eugenics to eliminate Down syndrome, other medical issues are becoming more common. For example, diabetes used to claim many lives before adulthood. These days, diabetics are able to live normal lives, including having children. Thus, they propagate the propensity for diabetes to future generations at a much higher rate than in the past. And in fact, diabetes is far more common today than a century ago.
Do we want to "disappear" our problems, or do we want to confront them, solve them, and learn from them?