Hey! *same boat*
I got a 169 on my first diag. My instructor came up to me and asked if I had ever taken the course or the LSAT before. No on both counts. So he had me see him personally on several occasions to give me advice. He said he thought I had tremendous growth potential and that I had the highest first diag. score he had ever seen. He too told me I should aim for mid-high 170s. I too doubted him. I was concerned about how anyone could improve after already getting nearly 90% of the Qs, since humans always have a margin of error.
I can totally relate to the pressure you feel. Although for me, it was more pressure I gave myself. Don't feel pressured cos of HIM! You don't have to ever contact him after the class if you don't want to...For me, the worse pressure came after my 3rd diag. when I scored 172. It was because I didn't know whether I had truely improved, or if the good score was a fluke. No matter what anyone said, the pressure wouldn't go away. I thought everything rested on the next diag., fluke or improvement? I got 167 on my next diag. I was devastated. But oddly enough, that made the pressure go away and the next diag. I went back up to 175.
I don't think anything anyone says could make the pressure go away. I think my long rant is just more to let you know someone was in the same boat and came out on top! Practice what you're worse at, and gradually you'll gain more confidence with your abilities.
(Oh, I too would LOVE to get into Columbia, that's the school I want the most right now as well)