The reason why the question of whether economics is a science is important because economists try to get a lot of mileage out of their claims that economics is a science. This gives their discipline an aura of scientific rigor that it does not possess, and often serves to allow economists to obfuscate un-empirical normative claims under the guise of a positive field (with an ample dose of technical language and mathematics to impress people who assume anything written in a mathematically rigorous manner is very Impressive and Scientific). For instance, monetary policy is based on economic theory that is totally unscientific in nature. There have been no major advances in macroeconomic theory, and for every major proposition x in macroeconomics there are "scientific" defenders of x and "scientific" defenders of not-x. Its almost literally impossible to follow decent scientific methodology when trying to explain and predict macroeconomic phenomena. Even technical advances in the field (like dynamic stochastic general equilibrium theory, etc.) have not done much. Even microeconomics struggles to even approximate a rigorous, empirical science. There are growing areas (behavioral econ, experimental econ) that are scientific, but most microeconomic theory is just not experimentally testable and is essentially just a field of applied mathematics. Financial microeconomics (the stuff that still basically follows the Valrasian paradigm) is a good example. If there was less fetishizing of mathematical notation and the bogus idea that economics is a hard science, maybe people wouldn't be so happy to put their retirement portfolio in the hands of a financial manager whose recommendations are based on a misappropriation of physics to attempt to model market behavior. Luckily, more and more people are taking the view that mainstream economics is not a science. To be sure, there are still quite a few people who look and see ALL THAT THERE FANCY MATH LOOKIN STUFF, are dazzled by it, and then dig in their feet and decide that economics is a hard empirical science, but those people are becoming fewer and fewer in my view. If we can ditch the idea that economics is a hard empirical science then our macro policy can receive the input it deserves from historians, ordinary people, etc., and our micro models can be viewed with more suspicion so that we are more appropriately wary when they undergird hundreds of billions of dollars in the economy.