MU is trying to allude to the contradiction in you definitions. If mental strength is defined in opposition to mental illness--
an absence of incapacity-- it cannot be the
response to present mental illness. In this case, it's impossible for someone to have mental strength and also a mental illness.
This is why "mental strength" has no apparent practical definition. In the terms of you definitions, it is not a response to mental illness, some action taken to deal with a present mental illness, but a
description of being in a state without mental illness.
Comment: The definitions allow the classification of all possible conditions of the mind as either being mental illness or being mental strength. — Agustino
You definitions preclude this because it would require that a condition of mind could be both a mental illness (incapacity) and mental strength (absence of incapacity).
Note: your direction is more or less correct, "mental illness" is a classification of ethics, a way of saying a particular way of thinking ought to exist. Rather than a description of a state of mind, it's a judgment about what sort of mind ought to belong.
This, however, amounts to an absence of standard in judging the presence of mental illness. In any case, we are relying on a ethic defined in-itself, rather than the presence of a mind.
In this respect, "mental illness" is revealed to be more rhetorical than anything else. It's a form a naturalistic fallacy. Instead of being honest about what at stake, a thought, behaviour or action which ought not exist, we equate what's wrong with the mere presence of body and thought. In terms of the individual, it's sort of a denial of responsibility. Rather than describe actions or states which ought not be (e.g. lack of motivation, despair, etc., etc.-- depression), someone is just said to be "mentally ill." It's nothing more than an image used to position where someone goes in an order-- e.g. the sorts of people who ought or ought not be, the sorts of people who need treatment or medication, etc.,etc.