Since I'm not on the UU council, my question probably will not be 100% correct, but here goes.
In my opinion, both Gothitelle and Wobbuffet were broken under the support characteristic. Gothitelle could revenge kill quite a lot of Pokemon easily with a Choice Scarf set, and the trainer would have no option but to watch their Pokemon die since they couldn't switch out. What makes this worse is the fact that Gothitelle also got Trick, which let it easily cripple a wall such as Chansey for the entirety of the game. Moreover, Gothitelle could even set up with a SubCM set (happened to me once) on a weak wall like Vaporeon (that had Toxic > Roar, very specific example ._.).
Wobbuffet on the other hand, could create many setup opportunities thanks to Encore, or could easily get rid of a Pokemon that only used attacking moves like Megacham due to Counter and/or Mirror Coat. This made it so it was too easy for a Pokemon to set up and sweep or that it was too easy to remove a huge threat from the game with little to no risk.
Again, I'm not on the UU council, so I can't say that this was the exact reasoning the council members used to ban Gothitelle and Wobbuffet, but I'm pretty sure it was somewhere around my version (hopefully :P).