Could bullets be easier to hit then missiles? I realize they have far less mass to hit but they also may move up seven times slower then a missile.
A round fired from a 44 magnum handgun travels at 391m/s OR 1407.6km/hr for the LIGHTEST load... or 460m/s (1656 km/hr)
A round fired from an M4 (5.56x45mm NATO) travels at 936m/s OR 3369.6 Km/hr
Now the average speed of a air to ship missile (since we are talking about CiWS systems) has a speed of 735km/hr all the way to 3000+Km/hr
The width of a .44 magnum round (the "fattest" round here and a good example of a heavy pistol round) is .43 inches the 4.46x45mm is less then half that.
The Width of the average anti-ship missile is .5 meters (1ft 7.5 in) to 1.4 meters (4ft 3.3 in) (for the fastest missile on record)
Speeds are similar.
Size different is MASSIVE. (and we haven't even talked about length),
Nor the fact that a CiWS takes up to 8 seconds to achieve lock on for a firing solution, which means the missile has to be deployed at ranges of 3km (for the slowest adjusted for safety margin.) to 10km (for the fastest, adjusted for safety margin)
In a gun fight in a urban setting, most engagements happen at ranges of 200 meters or less.... which means for more weapons, you are hit before you know you are under fire. Especially considering that the speed of sound is 343.2 m/s, means that the bullet has hit it's target before the rapport of the shot gets to the target.
There is no way to react in time to shoot a bullet with an other bullet in that time frame. when you look at the time needed to receive stimulus from the optic nerve to the brain, then the brain to process the danger, then sand a signal to the muscles, you are around .3 seconds (Providing of course you can see a 1.03cm object travelling faster then the speed of sound. AND, we have not even taken into consideration the time needed for your cyberware implanted computer (or threaded form) to process the speed and trajectory, compensated for gravity, AND factoring in your own weapon's trafectory, speed and compensating for gravity..... which, it you where lucky would be .1 to .4 seconds.
So now, you are looking at a response time of .4. to .7 of a second, and you are not even guaranteed to hit the target. meanwhile that bullet has traveled to you approximately 170.2m (If you react in .4 seconds) to 297.85m (if you react at .7 seconds) And that is for the 44magnum, using an averaged speed
If it was the assault rifle, in .4 seconds the bullet would have travelled 374.4m OR 655.2m if you reacted in .7 seconds.
Again, given that urban engagement happen at 200 meters or less... you hit with assault rifle everytime... and hit with the heavy pistol IF you are less then 171 meters from the shooter.
As said, physically it can not be done. And as Rhat points out, there is no cyber/bio or thread that allows you to either.
Not to mention that by RAW/RAI there is no mechanic for it either.