1998 Chevy Cavalier, Brake Problem

What would make the hydraulics on this brake system pulsate constantly, and make an odd clicking sound when stepped on HARD.
I am aware of an anti-lock sensor located somewhere.
But I'm confused by the clicking sound.
Facts are. I've replaced the pads on this car twice, had my local NAPA turn the rotors, then took the rotors back to them to be double checked.
The car is eating pads on the left, front at the rate of a set per year, and there are no fluid leaks.
I have kinda' already made my decision about what I'm gonna do. But my fix is expensive.
I wanna be second guessed.
......This forum ROCKS;-)....... The ABS system monitors all four wheel speeds by using wheel speed sensors on each wheel hub. It also uses the brake pedal switch as an input. When any of the wheels shows 0mph and the VSS (vehicle speed sensor) shows above 0mph when the brake it depressed the ABS hydraulic unit will dump or exhaust the brake pressure for that particular wheel(s) that shows 0mph or lock up. Once the ABS module sees wheel speed again for that wheel(s) it will stop dumping that circuit and allow brake fluid pressure to build back up. There is a hydraulic motor that builds pressure back up in the circuit(s) that had dumped and closed. The hydraulic motor is also used to keep the pedal from sinking to the floor and loss of hydraulic pressure in an ABS event. That is the pulsation that you feel and the clicking noises you hear when you stop hard enough to lock up your tires. The clicking noises are the valves in the ABS modulator opening and closing. The pulsation is the brake pressure change as the valves and motor cycle. The ABS system isn't designed to stop the vehicle faster but to enable you to have steering control in a heavy braking event. One thing to remember is that in an ABS stop you shouldn't pump the brake.
If you are wearing pads out faster on one side than the other than you may have a caliper that is sticking. Calipers should be replaced in pairs.Car Repair Talk's forum.