A frog and mouse battle

Back in the day (meaning the first half of the twentieth century), most mathematicians were deeply engaged in a dispute between two philosophies: Platonism and intuitionism. The details of the conflicting views are not important here; the main point is that both sides were arguing as if their respective positions were the true state of affairs, seemingly not realizing that the debate they were engaged in was of the sort which allows for more than one point of view to be correct. Upon hearing the details of the disagreement from one of his mathematician friends, Einstein reportedly called it "A frog and mouse battle." I have no idea what the thought process behind choosing this particular phrase could be, but nonetheless it seems to capture the essence quite nicely.

Economists have their own frog and mouse battle going on right now, and one that is substantially sillier than the original. It's the debate over whether or not GDP is the correct measure of quality of life. Fairly recently an international commission of economists led by Joseph Stiglitz (and created by the French President Sarkozy) released a report which suggested a measure of aggregate quality of life alternative to GDP. Numerous economists have then spoken up in defense of GDP as a better measure; one example can be found here.

I think there are two things that render this debate quite silly. First, I don't think there is a law of the universe saying that there has to be just one correct measure of economic performance. Quality of life is a multidimensional phenomenon, and different measures can and will place different weights on these dimensions, so I fail to see how a choice between those measures could be anything other than arbitrary. Second, GDP by its very definition is not meant to be a measure of quality of life. It's supposed to measure aggregate output, or, in other words, aggregate value added.

I really can't see anything other than a frog and a mouse in this debate. Am I missing something?