My three main points are:
(a) Mental disease is a metaphor, but mental illness is not.
(b) Feeling ill and having a physical illness are logically related. If there were no such thing as feeling ill, there would be no such thing as suffering from a physical illness. Yet there is no logical connection between feeling ill and being mentally ill.
(c) Mental illness is manifested in various forms of behaviour, for example, suspiciousness, elation, depression, etc.; if a form of behaviour is to count as mental illness, it has to be an insane form; yet it is possible to be mentally ill without being insane and it is possible to be insane without being mentally ill.