How do we fundamentally define what gets to be labled a social problem?
We fundamentally define what is labeled as a social problem in two ways.
First, we get to decide which conditions are good and which are bad. For example, it is a fact that there is a great deal of economic inequality in the United States. But is that fact good or is it bad? This is something that cannot be objectively determined. Therefore, we as a society must decide whether to define that objective condition (inequality) as a problem or as a good thing.
Second, we get to decide which conditions are problems that can be addressed and which are simply inevitable and cannot be fixed through our efforts. For example, it is clearly true that there is segregation in many American cities. But is this something that can be fixed or is it simply a natural outgrowth of people's desire to be among "their own kind?"
There are all sorts of conditions that exist in the world that can be seen as problems. Each society has to define for itself which of those conditions are problems (because they are bad and can possibly be fixed) and which are not.