You can be pushed out of your job without being fired. I believe it was a matter of philosophical differences between Brewster and Dunbar. IMO, Brewster made it clear that there were going to be some major changes to his system and he said, in his best Danny Glover/Sgt. Hulka impression, "I'm getting too old for this S***" and walked out.
In divorce terms it would be called irreconcilable differences.