I think Rodgers is waiting to see if another team, other than the Jets, will enter the ring, to make an offer for him. An opportunity for him to choose his landing spot, if he wants to continue playing.
In the meantime, he doesn't really care how it plays out as far as the Packers themselves. It's his ball, his game, and he's going to make the decision in his own favor, not caring what it means to the team, or anyone else.
At this point, it's his last chance to control what happens in GB, and I hate to admit it, but I don't think he cares at all how it damages the team.
Then, there's also the caveat where he decides to retire, and in August, decides he wants to play again, and removes his retirement papers. Then another drama starts, surrounding him.