As others have said, it's precession. But here is a way to better visualize it: Have you ever used a Spirograph? If you have, and drawn a pattern with a smaller geared wheel inside a larger geared ring, as the pen overall rotates the smaller gear clockwise, the gear itself rotates counter-clockwise:


The bottom bracket cup is the smaller gear, in the animation above, on the right (drive) side of the BB; As you rotate the spindle clockwise (under pedal force, a radial load that is constantly rotating clockwise), the cup precesses counter-clockwise, or to the left, so that's why you need left-hand (tightening) threads on the right side.