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I think we're calling the demise of Bug-types a little too soon. Yes, Fairy resists bug. However, Fairy doesn't hit Bug for super effective damage, and almost every bug-type that's worthwhile in competitive play has secondary STAB. Thinking off the top of my head, a mono-fairy type resists very few of those secondary typings.
Scizor, Forretress, Escavalier, Durant and Genesect all nail fairies with steel-type attacks and resist their attacks to boot.
Volcarona will still torch most fairies with fire-type moves. The only confirmed poke to resist both of its STABs is Azumarill, who gets hit SE by Giga Drain, Volc's most common coverage move. Sure, Aqua Jet makes it a strong check, but it was one already. A hypothetical Fire/Fairy type would completely cockblock Volc, but so far none have been confirmed.
Scolipede and Venomoth both have access to good poison-type moves to break Fairies down, in addition to resisting their STAB.
Other decent bug types like Galvantula, Scyther, Yanmega, Crustle and Armaldo all have strong secondary STABs that hit neutral, so I don't think they'll panic too much.
The only bug-types that really got screwed over here were Heracross and Accelgor (and Accelgor has the necessary movepool to adapt.)
Of course, fairy types with secondary typings could further complicate things, but until we know about those, I think it's wrong to write bugs off entirely.