Probably because Ice has a lot of weaknesses, so it's fairly easy to cover. The initial leaks said Fairy will be immune to Dragon attacks while being super effective against Dragons, though the former point hasn't been confirmed yet. Regardless, it's enough to make some people freak out. They're apparently forgetting Dragons can learn plenty of other types of attacks and Fairies won't be omnipotent by any means. Dragons will still be able to put up a fight.
If Fairy is immune to Dragon, it ends the latter's perfect coverage, the reason for its reign. And Outrage descends to obscurity.
Sylveon survived two STAB Hydro Pumps. In the Rain. From a Politoed. Now, IVs and EVs surely play a part, but that is freakin' tanky. Now special based Dragons are screwed: risk getting walled by Sylveon, or pack a Poison/Steel(rumored Fairy weaknesses) move to deal with it? Dragon users will be forced to carry a Fairy counter all the time, whether it be on the Dragon itself, or its teammates.
Now, until release we have no way to actually confirm anything, but it's a pretty good scenario to show why Fairy might be the Dragon killer.
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Fairy might literally be made as an antithesis to dragons -- from a myth standpoint, fairies can resist the elements pretty well, save fire (Which I still don't think they'll be weakened to b/c firefang/punch/blast are common dragon moves) . They could end up having 2~3 resists, 2~4 types they hit super-effective on, and maybe 1~3 types that hit them for super-effective (Poison/Steel/Dark being my wishlist there lol).