The forward blade on the UH-1 series went downwards with the main rotor down wash so it wasn't as effective.
Reversing the rotation meant that the forward blade went upwards through the downwash, effectively increasing the airspeed seen over the blade, making the tail rotor for effective.
Changing sides on the tailboom was the easiest way to do this, but it also changed it from a pusher tail rotor into a tractor tail rotor, so instead of sucking dirty air around the fin, it operated in clean air and just had to push it around the fin.
That is my understanding of it anyway.