This is a great question, and one I think we should ask more often.
I honestly believe that the only reason there is a stigma is because mental illness is not tangible. You can't see it.
Also, there is an illusion of control that exists. If you break your arm, you can't control the speed at which your body heals. But if you suffer from mental illness, many people assume that it's almost self-inflicted and is as easy as "just don't think about it".
Plus, mental illness is relatively new in comparison to traditional medicine. So naturally it will be met with skepticism.