How OP is Yi?

So, I was playing a Yi (first hard carry with Yi, I was pretty proud, even if we did lose the game), and the entire game, people kept saying "you're playing Yi, no skill." And I kept thinking "what? I have to repeatedly dodge your abilities with my Q, or else I get thrashed during a fight, I have to dodge your morgana's stun, so I don't get thrashed at the start of a fight, and I have to constantly dodge pretty much all of your skill shots, or else I get thrashed period." Not only that, they're toplane and midlane carries could both outduel me (I know, because I died to each of them during duels), and could easily destroy me were they to focus me. Not only that, Yi is easy as balls to counter with simple armor (and I wasn't even building armor pen, since I was forced to split push all game, I had to sacrifice two items for Banner and Zz'rot), something I know from wrecking Yi face playing as Nasus, Nautilus, and Rammus.

tl;dr Is Yi really as OP as people make him out to be?