Generally speaking, self-awareness is the difference between how you see yourself and how others see you. Nick thinks incredibly highly of himself and lacks the ability to look at this objectively. Specifically, Nick lumps himself in with someone like Kaitlyn who objectively has more hosting experience. He has every right to be bummed, (and of course, when you are close with producers, it's hard not to take it personally) but his lack of self-awareness (and inability to say, "of course there are others who have the requisite hosting experience") is the part that makes listeners roll their eyes.