The ACC voted against it because it was the B1G amendment that passed and not the ACC's proposal that the Big 12 joined. The ACC wanted to allow them to pick and choose teams to play in the championship game, which would allow them to split into 3 divisions and / or have 2 teams from the same division play in the championship game based on their rankings. There was also some speculation they might allow Notre Dame to play in an ACC Championship Game, although I don't know how credible those rumors were.
Why would the AAC vote against in in order to keep their league together? Cincinnati would have been a favorite to bolt to the Big 12 if that conference needed to expand to 12 to hold a championship game. I don't understand why the AAC voted the way they did, unless they are concerned that Navy is going to eventually reconsider leaving their independence. That would leave them as an 11-team conference unless they expand with another hardly desirable C-USA team. The round-robin requirement will make it nearly impossible to hold a championship game as an 11-team conference because it would require 10 conference games every season.