Authority is an interesting concept. In my experience, the most authoritarian of managers are usually the most insecure. IF Klopp/Shankly said something and the players did exactly what he asked them to, but the other team kept creating chances, I don't think they would be having a go at the players. Instead, they would be making tactical amendments. Rodgers instead was blaming the two defenders there despite them following his instructions. Doesn't matter if it's Klopp or Shankly, but if a manager does that, they will quickly lose the respect of the player. It's a hyper-competitive environment and managers succeed by being fair, and not by lumping the blame on someone else and relying on their authority for players to not speak up.
I agree with a lot of that.
To be fair, we do not know whether Agger was right or not. Maybe he was not doing what Rodgers had told him. It is not fair to just take his word for it. Rodgers has not had a chance to put his side of it.
Everyone gets it wrong occasionally, but there is a time and a place to challenge the manager and it is not half-time and rarely should it be done in front of the whole team.
Obviously, managers have different styles, but I do not see how you can tolerate something like that. especially at half-time when you have only a few minutes to say what you need to say. If other players see a teammate getting away with that it almost certainly lowers their estimation of the manager.
There is a time and a place for ranting and raving, but if a player contradicts you like that publicly then I expect the manager to give it to him both barrels.
I cannot imagine Klopp simply muttering "whatever" in that situation.
FAOD I am a big Agger fan, though I think on this particular issues he was wrong. It is a real shame his body was not up to the life of an elite athlete.