In accordance with NEC 440.22, the rating of fuse or circuit breaker for motor compressor shall not exceed 175% of nameplate FLA of motor or brach circuit selection current, whichever is greater.

1) My main question is that we usually set the rating of circuit breaker of 250% of FLA for usual induction motor but why 175% rule is applied for motor used for compressor.

2) What is branch circuit selection current?

3) Why does NEC require whichever is greater between 175% of FLA and branch selection current?

There are two currents used in motor calculations: FLA and FLC. One is found on the nameplate, the other from the charts in the NEC. One is used to determine the heater size, the other for determining the size of the conductors, the rating of the OC protection, the disconnect, and the controller.
The rational goes like this: The particular motor current draw will vary with the motor chosen and the load, but when you replace the motor, the branch circuit OC device, wires, disconnects and controller will remain. So the equipment and wiring are sized generically, but the OL heaters are fitted to the exact needs of the motor actually installed. If necessary, the fuse or CB is allowed to be bumped up to an even larger size if the motor chosen so warrants.

It may have to do with the service factor of standard motors versus compressor motors. Hermetically sealed motors do not always have the ability to handle overloading very well, so our protection has to be tighter.