We loose perspective when we look at a flat map. That big curved line we see on standard map is just too difficult for our minds to process. Often we tend to think east-west when the shortest route on a sphere just may be over the top, which is not well represented on a standard map.
And since you brought it up:
Last year I flew HKG-ORD:
Pretty amazing perspective. Consider that thousands of people fly that route without even realizing that part of their trip is over the Arctic Circle, which just a century ago was mostly unexplored.
Is there a website where you can plot points like you did?