Let's get something established right off the bat: Bruce Arians got himself fired by the Pittsburgh Steelers.
Tonight, HBO will air an interview in which the Cardinals' coach will blame Mike Tomlin for his unceremonious ending in Pittsburgh, where Arians was the team's offensive coordinator from 2007-11. In reality, it was Arians--not Tomlin--who got himself fired after refusing to listen to management, something the Rooney family finally got tired of dealing with.
Ed Bouchette of the Pittsburgh Post-Gazette has often reported that--on multiple occasions-- the Steelers' brass asked Arians to change the offense to take better care of Ben Roethlisberger, who was sacked 215 times during Arians' time as offensive coordinator. Arians refused and, despite Pittsburgh's 24-8 regular season record during his final two seasons with the team, Pittsburgh did not renew Arians' contract at the conclusion of the 2011 season.
Tomlin, fulfilling his role as head coach, had the unenviable task of giving Arians the news, and offered to fly to Arians' location to give him the news personally. In so many words, Arians told him not to bother, abruptly ending his time with the Steelers. And despite his recent successes in the years following his time in Pittsburgh--he was named NFL Coach of the Year in both 2012 and 2014--Arians is obviously still bitter about how his time with the Steelers came to an end.
Arians can be mad at the Steelers for not renewing his contract. He can be mad at Tomlin for not giving the Steelers the "keep Arians or I go" ultimatum, but he can't blame Tomlin for how his career in Pittsburgh ended. Arians' time in Pittsburgh ended because he refused to change the offense, which ultimately cost him his job.
Bruce Arians likes to run the show. He's doing just that in Arizona, where Cardinals' management gives him full rein to make decisions that he feels is best for the team. But, quite frankly, Arizona isn't Pittsburgh, where the team has to protect their future Hall of Fame quarterback (not to mention $100 million investment). The Steelers also have the Rooney family, who for decades have made decisions that have led to six Vince Lombardi Trophies. The Cardinals have won five playoff games in the last half century. Arians also wasn't the head coach in Pittsburgh, and he shouldn't have made Tomlin the middle man when he wouldn't just do what his bosses asked him to do.
In this situation, Arians has no scapegoats. He did a good job in Pittsburgh--the team won Super Bowl XLIII with Arians as the team's offensive coordinator. But his inability to follow authority led to the ending of his time in Pittsburgh. Arians still doesn't grasp this, and it continues to muddy his reputation in Pittsburgh, and further exhibit the arrogant and petty behavior that got him fired in the first place.