If you drive very roughly, you'll hurt the engine (and other parts of the car), doesn't matter it's automatic or manual transmission.
Nowadays, the computer is smart enough to protect the engine. For examples, it up-shift for you when you hit the red line, and it prevents you to down-shift it the engine speed is too high.
Sometimes, I think automatic hurts the engine. For example, if you're going uphill in D gear, and the computer doesn't down-shift to produce more torque, the engine needs to work harder to climb the hill.
I think your friend is jealous about the 6-speed +/- you have ;-)