Cause actually Korean also make many anti-grammartical sentence, this sounds pretty natural but it's not correct grammatically. You ignored parallel structure. You can say like this 노래, 요리, 춤 이에요 or 노래하기, 요리하기, 춤추기예요 or 노래를 하는 것, 요리를 하는 것, 춤을추는 것이에요

I would say 춤추기에요.