1) Mike Trout demanding a trade
I know, I know. Mike Trout has said all the right things publicly. There's a good chance he meant what he said and wants to remain an Angel no matter what. However, what if he does demand a trade? That'd be a nightmare for the Angels.
Let's start with the obvious. Trout is the best player in the history of this franchise. The best player in the history of this franchise wanting out would be a bad thing. Trout signed a deal to remain an Angel until he retired, watching him leave would be tough.
Taking the emotional side of this out of the way, a Trout trade would still be catastrophic for the Angels for a veryy clear reason. A trade would be almost impossible to work out so that everyone is happy.
Trout has a no-trade clause, meaning he'd have to approve a trade. Trout having the ability to essentially pick his next destination likely would mean he'd have a very short list of teams he'd approve of, giving the opposition all of the leverage in negotiations.
The next reason why a Trout trade would be catastrophic has to do with the return. What exactly can the Angels get for him? When healthy, Trout is still one of the best players in baseball. Unfortunately, Trout hasn't been close to healthy enough to be treated like one of the best players in the world in a trade. The injuries, plus the remaining expensive seven years on his contract make his value decline exponentially. The Angels will search for a king's ransom and likely won't get anything close. The Angels will also have very little interest in eating money to watch him play against them.
Trout wanting out would be bad for everyone. The Angels wouldn't get the package fans expect to really kickstart any sort of rebuild. Angels fans wouldn't get to experience Trout as just an Angel. It just doesn't work, so let's hope it doesn't happen.