To appreciate some of these implications, let's imagine a common, everyday situation. I intentionally picked a situation that someone may label as trivial. I will show that this is not at all a trivial situation. So, if we can show that this example is not trivial, then we are on a good path for understanding why economics is so special.
Imagine you are in a store buying apples. You see that the price of Red Delicious is $1.49 per pound, and that the price of Golden Delicious is $1.79 per pound. After some deliberation, you end up buying two pounds of Golden Delicious apples.
Can we explain what you just did? If we used economic principles, we would say that you valued two pounds of Golden Delicious apples more than $3.58 and more than two pounds of Red Delicious apples. If we asked why you valued them more, we could say that, given your goals, you judged that those two pounds of Golden Delicious apples would be the best means to achieve those goals.
However, if we went further and tried to explain your goals as a consequence of something other the fact that you are unique human being with a unique mind and free will, we are moving outside of the scope of economics. For example, if we tried to explain your goals as a consequence of your brain structure or as a consequence of your genetics or your overall history, we would be stepping outside of the scope of economics.
Moreover, if we contended that the fact that you bought two pounds of Golden Delicious apples and not two pounds of Red Delicious could be fully explained using objective facts like your history, your genetics, your brain structure, etc., we are claiming not only that there is no need for economics in this case, but that this event was not at all your choice--it was simply a consequence of the strict quantitative laws of nature.
If we extended this logic further to all human behavior, we would be claiming that there is no place for economics, the science of human choice, in explaining that behavior. According to this view, your behavior can be fully explained using the objective facts that surround you. You have no role in determining the course of your life. In other words, what you thought were your choices are not actually choices; they are simply a consequence of the strict laws of nature.
So, what's so special about economics? Economics is the only science that, not only acknowledges your freedom to move outside of the strict deterministic quantitative laws of nature, but uses that freedom as its methodological basis. You, as an individual with free will, observe the objective facts around you and then use your subjective judgment to evaluate those facts. Your evaluation of the reality around you is your choice. This evaluation determines your actions and thus guides your life path. The objective properties the world around you matter inasmuch as they are the raw material that enters your subjective judgment.
You might say that this is too extreme. What about, say, food and water; we are surely bound by laws of nature there, you might say. However, even in this extreme case, the laws of nature do not determine our actions, at least in the sense that these laws don't determine our preferences about life and death. It is true that if one wants to live, one has to eat and drink, but it is not implied in the laws of nature that one must want to live. Most of us have had moments in our life when we made a conscious decision to choose life over death. Implicitly, we make that decision every moment of our waking life.
Some individuals, however, have made a different choice. For example, some people sacrifice their own lives to save others' lives. It is also not uncommon that, during wars, people would rather die than be captured by the opposing army. Some people start hunger strikes for political or ideological reasons fully committed to taking their strike to its logical conclusion if their demands are not satisfied.
I avoided including the case of suicide in the above examples because it is commonly believed that suicidal tendencies are an illness with a biochemical background. However, if suicide was completely determined by the objective facts around us and by the natural laws that bind those facts, that is, if our free will had no say in it, then it would be an illusion to believe that suicide prevention efforts prevent anything.
Thus, if we assume away our freedom to choose, this would be a claim that we are just one more collection of molecules whose reaction to its environment is determined by the objective properties of that environment and the natural laws that bind those properties--just like the reaction of a stone rolling down a hill is determined by the objective properties of the hill and the law of gravity. This, however, does not mean that no human behavior can be explained using objective facts; it simply means that if some human behavior can be fully explained using objective facts, this behavior was not a consequence of human choice. This further implies that this behavior is not a subject matter of economics but of some other science, say, neuroscience or physics.
The special feature of economics is that it assumes you have some say in determining the path of your life. This may be a completely foolish assumption, but we will never know if it is indeed foolish. Even if it was, saying that scientific inquiry (including economic inquiry) makes our lives better would then be equally foolish and meaningless. It is irrelevant whether or not something makes our lives better if there was never any alternative.