Let's say you're in third gear @ 50 mph. If you were in second gear at that speed, your revs would be much higher. If you shift directly from third to second, you feel that lurch as the momentum of the axle / transmission pulls the engine up to the higher rpm. That stress on the engine is what you're trying to avoid. So in the middle of the double clutch, you apply the gas pedal and bring the engine up to speed the right way. Ideally, you get it to the rpm where it would be @ 50 mph in 2nd gear, but at least you're closer than a straight shift. Much easier on the engine to bring up the revs with the gas pedal than with the transmission.

someone tell me if I'm missing something.

that engine stress is not big deal ... in europe driving instructors will specifically tell you to actually brake on the engine ... it's the first thing they will tell you ... it has advantages...