I like Jeff, but I think there are three reasons fans expect more from him. One is his fault, one is sort of his fault, and one is not his fault at all.
1) The reason I expect more is because occasionally he has those monster games, that a lot of players never have. He's got the ability to do it, so I want him to do it more. He doesn't have to score 30 every night, or even 20 every night. But his off games shouldn't be 8. And they shouldn't happen as often as his 30 point games. I think that's on Jeff.
2) He's not a top banana, but he plays a position where a lot of teams find their top banana. The fact is in today's NBA, scoring comes from the 3/4 hybrids who can shoot from outside and explode to the rim. Green is that type of player -- he's just not as good at it. The expectations are partly due to his peers at the position, and that's somewhat on him. But Danny's right -- he's not getting paid anywhere near what guys who are better at that than him are getting paid (unless they're still on their rookie deal like Paul George).
3) He's replacing Paul Pierce. When Jeff Green has a bad game, I mostly get annoyed because I remember Jeff Green's good games, but sometimes also because I miss Paul Pierce. It's not Green's fault, but it's his lot in life.
Bonus Reason: Some fans delusionally think we would have won a title in 2011 but for trading Perkins, despite the fact that Perkins had not much in the tank that year and not much since, despite the fact that OKC has made one finals and won zero titles since Perk has been on that team with Durant and Westbrook and Ibaka, and despite the fact that Wade ripped off Rondo's arm in the playoffs. And they blame Jeff a little bit for this.