May apologies if I sounded knee-jerky. The intention was to show that a picture was a better answer to @dbatten's very legitimate comment.
The idea is to demonstrate that a "straight" line on a surface needs to be viewed along a normal to that surface at the point of the line you are concerned with, assuming the definition of "straight" is "don't have to turn when travelling along line on the surface". That makes great circles look straight, and non-great circles not.
The idea is to demonstrate that a "straight" line on a surface needs to be viewed along a normal to that surface at the point of the line you are concerned with, assuming the definition of "straight" is "don't have to turn when travelling along line on the surface". That makes great circles look straight, and non-great circles not.