This prejudice is flawed. It fails to acknowledge that the mind also has unconscious elements outside of direct control. For example, a susceptibility to depression is part of the structure and function of the brain. This is part of our thrownness (the state in which we exist) and thrownness is blameless (in the same way we didn’t choose whether we were male of female).
Despite having no choice over the fact of mental illness, we are not helpless: we can choose our reaction to it in the same way we choose to put a plaster cast on a broken leg to help it heal.