The danger is in that e-juice producers don't label their products, and they may contain fragrances and chemicals that are harmful to felines, while considered safe for humans. Some e-juices contain Oil of Peru, for example, which is highly allergenic, especially to cats. Even if the cat does not react now, repeated exposure can trigger an allergic reaction later.
VG can be a lot of different stuff too. Glycerol contaminated with diethylene glycol is not unheard of, and while testing of food and medicine glycerol is mandated, there are no such restrictions on e-liquid.
Unless you know the ingredients in your e-liquid, and I mean better than "PG/VG/flavors", I would not recommend using them around sensitive pets like cats and birds.