In one of my very first lessons in uni, I answered a question with "I think … " The teacher said, "No one cares what you think." He was a nice man and wasn't being mean — but he was right: Everything I said or did at uni for the next three years had to be backed up by reading from people with some earned credibility and had to be balanced and supported by stats and facts. It was a life lesson that has held me in good stead in my career, too.
Second was when I was learning to write news stories (studying journalism) and the teacher, who was a former editor of a local paper, came and looked over my shoulder. He said, "I think we know what needs improving here," leaned over, took the mouse, and highlighted the copy. He then just hit "delete" on all of it and said, "Start again." He wasn't being funny and was completely deadpan in his delivery. But he was right: Sometimes it's better to just start fresh.