Why does everybody love cats?
Sounds unnatural (grammatically broken). I guess the author (translator) of the Japanese sentence is not a native speaker.
My alternative translations are:
なぜ皆、猫が好きなのですか？ Note: simply modified based upon the original Japanese sentence.
みんなが猫好きなのはなぜですか？（みんながねこずきなのは…）= (lit.) Why is everybody a cat lover?
皆、猫が好きですか？(Does everybody love cats?) is grammatically correct. But when you insert “why” なぜ into this sentence, you need to convert 好きですか into 好きなのですか.
皆（みな）sounds very formal, and it can even implies that the speaker hates cat lovers (i.e. condemning, undermining or interrogating tone).
猫好き (a cat lover) is a frequent set phrase. I personally prefer the second one. It sounds more natural.