Many things in large quantities can be toxic. Many companies claim they use REAL essential oils in aromatherapy products, but they do not, or they use oils which are cut with synthetics.
The essential oils I am talking about are not called "natural" or "fragrance"
Pure, good quality oils are available as single essences (and some mixes) from reputable companies like Aura Cacia.
Of course, anyone can be sensitive to anything.
True good quality essential oils should always be heavily diluted with water or other oils, or sometimes alcohol. I have been making my own cleaning products and holistic health remedies using many different essential oils for years.
I can assure you that I am extremely chemically sensitive - to the point that I sometimes cannot be in the same room for long with people who use cologne. I cannot be around leather furniture for long (due to chemicals used in the tanning process,) or any pesticides without getting sick FOR DAYS.
However, I have used essential oils (properly) for years with absolutely not one issue whatsoever, and my dogs have never suffered any ill effects, either. Cats are a different story.