By far that they can, "Give you CANCER." Someone literally said this to me with a straight face, while looking at some of my hatchlings at a local expo. I am a biomedical scientist, and it took every ounce of me to not scream at this person.
Growing up I had a cleaning lady who told me that birds can give you cancer also. Not sure who is perpetuating this exotic animal and cancer link, but it is ludicrous.