At what point is it a sin?

At what point does self-pity/depression become a sin?

Probably when you enter into it with free will.

As opposed, for example, to someone who is depressed due to a chemical imbalance in their brains that requires medication (or even doesn’t improve with medication) and is beyond their ability to choose or control.

In addition to the above statement, also when you reach a point where you actively decide not to try to fix the problem. If you recognize that you are depressed and don’t try to correct that issue, then you might be committing a sin. You should really speak to a spiritual adviser to dig into this question on a more personal level.

In what possible way can clinical depression become a free choice? Is bipolar disorder a free choice? Is any mental illness a free choice?

The best answer you can get is to go to the nearest Catholic Church Rectory and ask to see a priest. You can do this at any reasonable time of day.
You will be amazed at the reception you will get!

Depression is not a sin.
Despair is a sin.

The two are different.

Modern catholic Dictionary:

DEPRESSION. A term used by spiritual writers to describe a state of despondency during which a person feels inadequate, tends to withdraw from others, lacks response to normal stimulation, and is pessimistic about the future. Theologians of asceticism warn about giving in to moods of depression, which they describe as the characteristic of temptation of those who strive after sanctity.

DESPAIR. The sin by which a person gives up all hope of salvation or of the means necessary to reach heaven. It is therefore not mere anxiety about the future or fear that one may be lost. It is rather a deliberate yielding to the idea that human nature cannot co-operate with God’s grace, or that the despairing person is too wicked to be saved, or that God has cast one away. It is a grave crime against God’s goodness. Experience also shows that a tendency to despair can seriously injure one’s physical and mental health, and ironically can lead to all kinds of sinful indulgence. (Etym. Latin de, the opposite of + sperare, to hope: desperatio, hopelessness, despair.)

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