I think the default assumption, by common sense, is that psychopaths are more frequently violent than anorexics. If you have data to suggest there is no difference in violence, that would be very curious, but interesting.
But that is not what you said. You said that “there are some mental illnesses that greatly increase the chance of a person harming others”. Your exact words. Now you are contrasting the frequency of aggression across diagnoses, which is an entirely other issue. Probably can find that info on the CDC website.
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My “exact words” need the front half of the sentence.
A particular mental illness - psychopathy (for example) - greatly increases the chance (I surmise) of the person harming others (relative to anorexics, for example, and people with no mental illness).
I don’t see anything controversial in associating levels of violence with some types of mental illness.
An eating disorder is not a personality disorder. But whatever. Not worth trying to explain.
^I made no reference to an eating disorder being a personality disorder.
You lumped all mental illness into one. They are not the same. A muscle strain and a brain aneurism are both medical diagnoses, but they are not the same. Moving on…