>It’s not halfway across the globe

Equator is 40k km long, so it makes sense getting "halfway" there would be 20k km. But the "half" is of something, and it doesn't sound right that "at the end of the globe" would be the same place you started with. Especially since being "on the other end of the world" means roughly, well, opposite side of the globe.

So I think OP is justified in defining "across the globe" as the "opposite side of the world", and then "halfway across the globe" is "quarter the length of equator away". But maybe I'm overthinking it.