He is just trying to pressure the Warriors to give him a max contract as he is part of the big 3, it's just unfortunate that his performance is not so impressive in the playoffs although they won the championship. However, in the end, it still depends on the decision of the Warriors if they will give him a max contract or not, and it's also up to Green if he will look for another team to give them what he is asking for.
If you had said Draymond Green was part of the big trio a few seasons ago, I would have certainly agreed with your statement. However, based on last season's results, Green's performance hasn't been impressive, and he's definitely not part of the big trio anymore. Maybe some will disagree with me, but it seems to me that Curry, Thompson, and Wiggins can be named as the Warriors' big trio at the moment.