Claudio Bravo decided to leave Barcelona because he didn't want to stay on the bench. That's not something I made up, it's what Bravo himself says.
The Chilean keeper gave an interview to Catalan radio about his decision to move away from the Blaugrana to join Pep Guardiola and Manchester City at the final days of the summer transfer window. After two spectacular seasons as the league goalie, Bravo was set to become a backup keeper to Marc-André ter Stegen, as the German would be given the undisputed starting spot for both league and cup matches.
According to reports, Bravo then chose to leave the club, and even though Robert Fernández offered him a better contract to convince him to stay, he wanted to play regular minutes and finally accepted Pep Guardiola's offer to play in England.
This was all rumors, however, until Bravo finally confirmed this is exactly what happened:
"It was not me that was [first] at Barca, it was Ter Stegen. The club made me an offer to renew but, seeing their plans, I also made them understand my position. I was very sincere, I did not want to sit on the bench. It's not my thing. And they understood. In Barcelona I always devoted myself to doing my best, I always felt the support."
Even though Ter Stegen was the reason why Bravo left the club, the Chilean insists he did not have a poor relationship with his former teammate, but their competition helped both become better players.
"What appeared in the press – that we had a bad relationship and things were uncomfortable at the end – was not true. It was never a problem, indeed, we both always benefitted from the competition."
Bravo, source: Cadena SER via FourFourTwo