As some have alluded to it is because of the concept of the great circle. In short, the great circle can be imagined by cutting the globe in half with the the center of the globe, the origin and destination on the plain created by cutting the globe in half. As on a flat plain the shortest distance between two points is a straight line; the shortest distance between two point on a sphere is on a flat plain.
The plains are pretty flat but you meant “plane”.