As stated in the title: why can asymmetric thrust occur for Single-propeller-engine airplane at idle-power during stall practice?
The phenomenon you speak of is called P-factor. It is the result of a non uniform angle of attack for the propeller blades throughout the propeller disk.
A typical piston powered single engine aircraft has a propeller which turns in a clockwise direction as viewed from the cockpit. In this fashion the propeller blades are ascending to the left of the pilot and descending to the right of the pilot. During straight and level cruise (high speed) flight where the airplane’s angle of attack (AoA) is minimal the propeller blades on the ascending and descending sides of the propeller disk have approximately the same angle of attack as they rotate causing the thrust force to be uniform over the entire area of the propeller disk. But as the airplane enters a higher AoA either when maneuvering or maintaining altitude during slow flight, the angle of attack for the propeller blades on the descending side of the propeller disk have a greater angle of attack than do the blades on the ascending side of the disk. This causes the blades on the descending side to generate more thrust for a given engine speed which results on an uneven thrust loading over the entire propeller disk, resulting in a counter clockwise torque about the airplane’s vertical axis. P-factor is most pronounced at high engine power settings at the critical AoA for the airplane where the thrust asymmetry is most acute.
P-factor plays an important part during multiengine operations as well. When an airplane had two or more wing mounted engines all turning in the same direction, there is always one engine such that, if it should fail, the yawing moment generated by the P-factor of the remaining running engine will be the greatest as compared to if the engine which is currently running had failed instead. This engine is called the critical engine and creates the most difficulty in maintaining directional control should it fail.
If attitude is strongly nose-high, the propeller push of a single-engine plane may have a significant asymmetry between the left-half and the right-half of the disk. It may have some yawing effect, but that can't be important at idle power...