The level playing field is a metaphor often used in debates about fairness and opportunity in the United States of America. It refers to the fact that the purpose of government intervention is not to give aid to specific individuals or groups of people (teams), but rather to make sure that everyone can compete fairly to the best of their natural ability.
The silly and yet somehow earnestly good natured part about this belief is not that Americans think they have a level playing field, but that they think such a concept is possible or even meaningful. The belief in a level playing field comes from a centuries old held concept, developed most fully in English speaking countries. The belief is the belief in atoms and the void, that the world is a tabula rasa, where a natural order exists, with a few basic natural laws, and independent agents, be they atomic particles or consumers exist in that field of natural laws, and react in it according to that set of laws. The term billiard ball physics has been used to describe it, and the term billiard ball sociology would make sense in describing social and economic analysis that use this theory.
The problem is that we, as a society, were not just plopped down into the world willynilly at random and then left to interact with it according to whatever our libidinal desires. We created the world around us, and we continuosly create and recreate it. The system of individual employment is not "natural". Our network of freeways is not "natural". The Nuclear family is not "natural". Public education up to the 12th grade for free, but not beyond, is not "natural". Whether any of these things is the best way to live is another issue entirely, but to pretend that they are "just their" and that we just happen to be reacting to them is unconscientious, to say the least. Their is no level playing field because their could not possibly be a society, almost by definition, that did not alter the "natural" world.
To return to the metaphor, a level playing field for who? If a group of crosscountry skiers and a group of downhill skiers were to have a race, would a level playing field be a level playing field?