I consider myself a moderate conservative and have always found these equations offensive also. There are extremists on both sides, it is usually the moderates who come up with the practical solutions.
Then you get into the definition of what is the "right" or the "left" which varies from country to country.
President Obama is considered "left wing" or a "socialist" by many americans, but his policies/ideas are perfectly aligned with those of our Conservative Party which is considered "right wing" by Canadian standards...