1) Berry Juice
Some people argue that the juice is not as broken if you just take away the combo with Sturdy, but Pokemon with Unburden and Acrobatics (aka the biggest offenders, generally, of gligar and swirlix) can still take advantage of this item. It basically gives a huge boost to sub and setup sets and gives already super-powered Pokémon amazing recovery. I have the same reasons as most other people to ban the heck out of this fermented stuff. Pokemon that run bj and already have great bulk are just a nightmare to take out in general, although fake out and knock off help mitigate things. Those moves can still be fairly easily predicted.
2) Swirlix
I love this Pokémon, but it's just really hard to take down and its versatility and speed make it a sweeping demon. People are usually required to run a steel or poison move just to reasonably handle this beast, along with maybe a fire type or another swirlix. Unburden is great in a meta game full of knock off and consumable items, and Swirlix is awesome even without berry juice recovery. Swirlix does, in most cases, stand a fair head and shoulders above most other LC mons. Get it out of here.
3) prankster+confusion
Prankster itself isn't that broken, but monsters like murkrow can easily use Para-fusion to wreck momentum. This wouldn't be so bad on its own, but if swirlix and gligar are banned (and it looks to be heading in that direction for nominations at least) then other mons just won't be able to dispatch the worst offenders as easily. The main thin this combination has going for it is the healthy presence of Chinchou and to a lesser extent Magnemite and things that use Wild Charge (maybe I run calcs later)
Gligar is really versatile (setup SR, aqua tail, etc) and fast and has increased the amount of ice moves being played on its own, mostly, but there are some hard counters like Chinchou, Porygon, and Meditite.
So I have nothing super new to say but... I like to justify my answers :/