Left and Right have nothing to do with the state (they both want to use the state for some things and want the state to stay out of other things).  However, left and right are a real division in society.  They are lifestyle choices.  Right now we have two sides fighting to impose their lifestyle choices on each other.  The only commonality in this fight is that they both want to use the force and violence (aka government) to impose their will on the other side.  Thus the left/right paradigm inherently drifts towards statism as both sides demand state violence be used against the other.