I was taught that if you want to change the direction of a three phase rotating machine that is rotating in forward direction, you interchange the phases. Since the phases has the same features (voltage and current), what is responsible for making the machine to rotate in reverse direction, when the phases are interchanged?
The windings in a 3 phase motor, when activated by a 3 phase supply produce a rotating magnetic field in the rotor area of the motor. Swapping phase A with phase B re-orders the fluxes so that the flux rotates in the opposite direction. Swapping B with C does exactly the same thing as does swapping A with C. Think of it like a triangle with corners called A, B and C. If you swap any two corners and follow the points A, B and C you'll go in anopposite direction. Swap two more corners and you're back to the original rotation.
This is what it looks like. The black arrow is the flux produced by the three phase windings: -
Clearly, if yellow phase were swapped with blue phase the rotation would be opposite.
The phases have a phase shift of 120 degress - called electrical phase angle, meanwhile the windings on the motor are also shifted by 120 deg - mechanical angle. In a such way, when the current passes trough windings the rotating magnetic field is formed, which is the sum of all three vectors. This is the principle of induction motor that Nikola Tesla made 130 yrs ago.
If you simply swap two wires, the magnetic fieled changes the direction of rotation.