A helicopter flies off, its propellers rotating. Why doesn’t the body of helicopter rotate in opposite direction?

Helicopters always have two propellers:

One is the main rotor, and another is the tail rotor to counteract to torque of the main rotor. If the tail rotor fails, the helicopter will start spinning out of control. Ex: Chetak, Cheetah, HAL Dhruv, etc.
Two Main rotors; either one above the other as in Kamov helicopters, or one behind the other as in Chinook helicopters; in such case the two rotors rotate in opposite directions to cancel out the torque effect from each other.

Regarding propeller aircrafts:

In multi-propeller aircrafts with multiple engines such as the Tupolev Tu-95, the propellers again run in opposite directions to each other.
In single engine planes with propellers, their flaps/ailerons and vertical stabilizer are adequate to counter the propeller torque.

Not an exhaustive answer, but enough for the above question.