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When you do anything with the system that requires fluid flushing, whether it's putting in new pads, or just flushing the fluid, you risk damaging the master cylinder's internal seals if you use the pedal pump method. Pushing the pedal downward even slightly beyond its normal travel risks moving the piston's seals into areas of the bore that will scrape the seals and destroy their integrity. Then, after you finish the job, when you push down the pedal, fluid is able to recirculate from the cylinder chamber (that you're pressurizing to stop the car) back to the reservoir. It feels like you've got (a) an air bubble in the lines if the pedal is just spongy, or (b) a fluid leak if the pedal drops to the floor; but in either case, its just a master cylinder with now defectivie internal seals.

This is why the preferred method is to use a pressure (or less desireable, vacuum) device to flush the fluid (the former on the reservoir cap, the latter on the nipples). Neither moves the brake pedal (and the master cylinder's piston), keeping the master cylinder safe.