With the exception of people who commit suicide in terminal end-of-life situations (terminal cancer, or similar), folks who are attempt or commit suicide because of depression, aren't thinking straight. The depressed brain senses, feels and interprets things differently than the same brain not depressed. So the idea is that the person isn't well, and their decision making process isn't working right. The decision to commit suicide is the result of hopelessness brought on by the brain misinterpreting the person's situation and perceiving that the only way to escape the situation is death. The person doesn't want to die, per se. They just want the pain to end. With that in mind, to allow a depressed person to commit suicide is basically failing to treat a person's health problem, and them dying as a result of it.
I'm a proponent of allowing people to make that choice when they have the wherewithal do so. Someone who is dying of a painful terminal illness, etc, end of life is no one's choice but yours. But the suicidally depressed person can't make that decision rationally. It's like making any decision under the weight of extremely strong emotion, only it's an order of magnitude more powerful than what most people will experience in their lives. The suicidal person is ill, and needs help. It's the fact that they can't find help that brings them to suicide.