To answer only the question of why right cups have left threads, which at first glance seems counter-intuitive, you need to understand something of the character of ball bearings.

Draw a quick sketch of a simple ball bearing assembly, consisting of a small circle surrounded by a bunch of smaller circles, and surrounded by a ring. If the inner circle is spins clockwise, each ball will spin counter-clockwise creating a counter-clockwise reaction force on the ring. In machinery where ball bearings are not properly restrained it isn't rare to see the outer race walking backwards slowly while the shaft is running at high speed.

The same logic explains why left cranks are left threaded, and rights are right threaded. A quick analysis will reveal that this is bass ackwards, since the relative motion of the right pedal to the crank should unscrew it, and likewise on the left. The reversal of torque through the BB explains why, and also explains why if the bearing gets stiff or seizes the pedal rapidly unthreads. It's an interesting quirk which seems to get rediscovered periodicly whenever somebody decides to replace BB pedals with plain bearing (bushing) models.