You can, actually. The RN's Sea Wolf system is recorded as having successfully intercepted a 4.5" shell during trials, and I believe that there's an American system based on the Phalanx CIWS that can hit mortar bombs in flight. It would be fairly easy to overcome these with enough incoming rounds, and cost-effectiveness is probably low, but at least in some situations it is possible to defend against artillery.
It doesn't matter if it is
able to shoot down a bullet, it must be capable of doing so
consistently. And even if you do have a system that can shoot down artillery shells, 100% of the time, it loses logistically since the interception system will always be more expensive than the artillery, for the following reasons:
An artillery piece only needs to be able to do 2 things: propel a mass over a distance, and calculate the arc needed to hit a stationary target (or one moving in a straight line) with said mass. These things are not hard, they were doing it in ancient Rome. Fire, see if you've hit, adjust if you missed. Bullets are cheap.
To intercept the projectile, you must be able to quickly calculate its trajectory, the trajectory to interdict it, and then fire the interdictor,
all in less time than it takes for the projectile to hit you. To do this, you must know the projectile's speed, mass and aerodynamic profile. You must know the atmospheric conditions affecting the projectile along its course, and the atmospheric condtions along the course of the interdictor. You may have to compensate for the coriolis effect.
This calculation must also take into account how long it takes to calculate itself, because this will affect where the projectile is, and where the interdictor must be aimed. Thus, the targeting for the interception system required far more energy, and will thus prove more expensive.
With missile interdiction, it is quite possible for an interception system to be cheaper than the projectile. With artillery, it is not.