Burning candles also releases VOCs (and soot) into the air. My old roommate was a daily candle burner, and the walls in her bedroom ended up absolutely covered in soot after a few years.
Not only that, many (but not all) essential oils are very toxic to cats and maybe other pets too - blanketly calling them "safe" is just plain wrong. Like very, very wrong.
It's probably not a good idea to diffuse essential oils in general, they are VOCs after all, but it's an especially bad idea if you have pets.