From what I understand, running LOP has been an controversial issue with a lot of misinformation and a lot of old pilot tales about the dangers of LOP operation.

I think LOP gets a bad wrap because pilots attempting LOP damage their engines by not having the proper equipment to monitor their engine temps, use bad fuel, don't enrich for high power, or they have another issue in their aircraft that isn't causing the engine to get enough cooling.

Your instructor is probably telling you to run ROP because there might be a restriction placed on LOP operations by the aircraft owner, the instructor wants you to focus on other things as part of your training, and of course he's not paying the fuel bill. You may at least try to convince him to run lean on the ground, since running full rich during taxing can foul the spark plugs. Maybe it'll open the door for an honest talk about LOP?

Found a great slide on LOP from the EAA, if I was an aircraft owner and I had the proper engine monitoring equipment I'd definately get someone familiar with LOP operations to show me how to do it correctly. The fuel savings are huge (and if done properly, the engine runs healthier as well) Running Lean of Peak