It is more of a metaphor. Only actual organs in the body can be sick or ridden with a disease and since the mind is not an organ that can be seen, it cannot be sick. The psychiatrist has the power to decide that the person is not competent enough to function well in society and that treatment is needed and they can do this without the person's consent to do so. If the power to determine the mental welfare of people is taken away, then so is the power to decide that the person needs treatment without consulting the patient beforehand. This leaves the person with his personal liberty to make his own decisions and lets him live freely, the way everyone should be able to live.
Every solution always has problems to it.
Not everyone is going to be pleased by this solution and that is, of course, to be expected. While it may please some of the public, the other part may see it as dangerous for society. Psychiatrists would not like it because it shows them as incompetent and the government would not like it because they would not be able to justify putting suicidal people away from the rest of society. This solution may please part of the public because it gives people their personal liberty of choice, the other part may see it as dangerous for society as a whole. They may see it as dangerous because if the suicidal people were left out on the streets, they might cause harm to themselves or to other people.