This is a complicated issue in part because the terminology involved often has different meanings to different people. Further complicating the issue is other words, often with ambiguous meanings, get thrown around interchangeably with left and right, like liberal and conservative, which are related but different concepts.
If you look at the historical meaning of left and right, the "right" can be divided into two camps: the first believes there should be a certain hierarchy of power and wealth in a society, the other believes there naturally will always be a hierarchy of power and wealth. The "left" can also be divided into two halves: one believes that all inequality is inherently unjust, and the other believes that certain types of inequality are unjust and in general there would be much less overall inequality if certain unjust systems weren't in place.
I like to think of left and right primarily as perspectives on life, that don't necessarily imply one type of solution or another. There are views from the right and left that advocate large government and centralization of power, and there are views from both sides that advocate total decentralization and voluntarism. This could be described as statism/monarchism vs anarchism. Yet another philosophical divide is individualism vs collectivism. Extreme individualism requires anarchism, but that doesn't mean all anarchism must involve extreme individualism. Similarly, extreme collectivism requires extreme statism, but not all collectivism has to be statist.
The extreme right (there should be hierarchy) and extreme left (there should be total equality) tend to go hand in hand with more authoritarian, statist approaches. On the other hand, in the broad middle, you'll find views the advocate centralization of power, as well as views that advocate decentralization and individual liberty.
The media and politicians play on emotions and wedge issues, IMO, to confuse people and control the terms and scope of the debate. FOSS is interesting, because it's an anarchic model with decentralization of power and decision making, completely voluntary hierarchies, and it incorporates some collectivist principles, yet also a strong focus on individualism and total choice.