Left and right are just slurs competing Totalitarians use against each other.
The real dichotomy is between Totalitarianism and Individual Freedom.
What you stated there is exactly what the Left wants you to think, that the right is simply a mirror image of the left, and I have never thought that to be true.
I have thought the political spectrum is TOTAL government on the Left, and NO government on the Right, but having never taken a political science class, I go on things like this I have read or watched over the years: The Political Spectrum Easily Explained: Basic Forms of Government
But I have heard criticisms of this as well.