Sure, you can leave it on. In fact, that's one of the marketing schpeals GM is using to tout the remote start feature. Leaving the A/C on when you shut off/start the car doesn't do anything. The system doesn't actually engage the A/C compressonr until after the computer detects a stabilized start (you'll hear the TICK/CLUNK noise a couple of seconds after the car starts if you've left the A/C on). So no, leaving it on won't hurt anything - your dad has strange ideas. Interestingly enough, my dad thinks the same way, only he turns it off 5 minutes before we get home LOL!