A person who is suicidal is likely to be depressed, and part of depression is pessimism--an unfounded belief that things will not get better. So chances are that a person who sees him or herself as rational for wanting to stop living is actually irrationally imagining a future that's much bleaker than it will really be. That's not to say there's never a case in which the future is, realistically, terribly bleak. In those rather rare circumstances, is there any good reason to go on living? There are certainly considerations that could weigh against taking one's own life. Suicide has a major impact on others besides the person who dies. Perhaps a person is needed by others, or the suicide would be terribly traumatic for others. That may or may not be decisive for someone in a specific situation, but I can imagine cases where it would be a "good reason to go on living" (as you put it). It goes much further to say, like some philosophers (Kant, for example), that there's something inherently unethical about committing suicide, so that choosing to die is always wrong, no matter what.
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Suicide is often said to be irrational or immoral. But what good reasons does a person have to go on living if they are unhappy and have no reason to believe that they will ever be happy? Isn't the opposite often the case that the choice to live is in fact more irrational than the choice to die?