I agree.He challenged Akainu for the position, since he thought Akainu wasn't right for the position. After losing the fight, there was no way Aokiji could serve under a person he does not acknowledge as his leader.
He left the Marines, meaning he quit his job. Early retirement. Simple as that.
He did not turn criminal, he quit like Sengoku and Garp. I don't see why he would want to go up against the very Marines he was a part of, simply because he does not acknowledge the new leader. It's not like he defected from the Marines and turned traitor.
Aokiji does not agree with Akainus sense of justice, but he knows its still justice. Akainu would have to do something REALLY outrageous as Fleet Admiral for Aokiji to join a pirate crew or Revolutionary Army in order to go up against Akainu and the government.
It just won't go right for him to join either of Garps descendants.
Kuzan is either retired n chilling or he quit and is sailing doing something no one has any idea on.
He'll show up, hopefully as a neutral party.