I had this realization some time ago, but I didn't get around to discussing it until now. The media and mass-minded people (Albert Jay Nock gave me that phrase) think in terms of left-wing and right-wing politics or political opinion. It also encompasses social and economic opinion. Left-wing are the progressives, and right-wing are the conservatives. Left-wing policies include welfare provision, state control over medical care, heavy regulation of most industries, environmental laws, and so forth. They also include much less foreign interventionism. The right-wing policies are basically the opposite. The main different between the two, then, is not the extent of state involvement, it's the geography. Further, right-wing policies include state interference in peoples' daily lives for the purpose of increasing the security of the nation (think TSA).
The division is false because both right-wing and left-wing policies are statist policies. The proponents of each want to use state power to control people, albeit for different ends. The true difference is between pro-statists, and pro-individualists. Individualists (aka libertarians, voluntaryists, anarchists) want to not use state power. Individualists want to use methods of peaceful exchange to accomplish their goals. To the extent a government is needed, individualists want such a government to be limited and responsive and to be a servant of the people that created it. This is the opposite of what we have today.