When I move lever on the remote to the right the rotor blade turns but when I turn it to the left it doesn't spin at all.

It's suppose to do that.

I guess I could explain it. The tail rotor doesn't need to turn when pushing the stick left because the torque of the main blades will turn the heli. Only when you need to give it right stick does the tail give input because it needs to fight the torque of the main blades to turn to the right.