What makes you think Bravo was just a "back-up" keeper? He was one of the best keepers in the league already. It was clear that they would be competing, I don't buy that you haven't seen this coming when he was appointed. Barca gave green light for a long term playrole for him, when Ter Stegen hasn't even played a single competetive match for Barca yet and ter Stegen's injury lasted WEEKS at best. It wasn't like he was out the entire first half of the season.
Yes, it's the boards job to ensure that Barca works, after all no player is bigger than the club. But that doesn't excuse them from luring players like that. That IS selfish. I know that there are wrong and right reasons for Barca to appoint Bravo and that he had also deserved the playtime, but from Ter Stegens perspective alone this was simply a punch in the face, and we all know it. This is singlehandedly supported by the fact that he is now giving an interview about his unsure intentions about a future at Barca.
This is simply what it looks like to me: Barca signed Ter Stegen, a young upcoming keeper, after Valdes decided to leave. He looked good at Gladbach, but Barca was aware that this is a risk and a possible flop would be lethal. So in order to cover their own asses, they decided to go with a second goalkeeper, an experienced one on Ter Stegen's level. Not as just a back-up, but as actual competition to see who actually performs better. After all it was a piece of safety for just 10m. It's no doubt a smart move from the board, the signing of Bravo was absolutely great. It just wasn't great for the other goalkeeper who signed earlier had no idea, that Barca is now doing the same that Madrid had done earlier with Casillas and Diego Lopez.