Right and left wing are historical terms stemming from the literal left and right halves of a physical building. If you’re not referring to the revolution era french national assembly, you have to accept that since other connotations may have snuck in along the way.

Even at the time the terms came with complex meanings.

Boiling it down at any time merely to equality versus hierarchy is only something you’d do if you want to misrepresent people by oversimplification.