The morality of suicide is an issue that has divided philosophers for centuries. The ancient Romans, for example, seem to have held the credo of “death before dishonor” in high regard. Two of history’s most famous suicides are those of Anthony and Cleopatra, who took their own lives after their forces were defeated at the Battle of Actium in 31 B.C. The Roman statesman Brutus also committed suicide after a military defeat, and Cato the Younger took his own life to protest Julius Caesar’s dictatorship of Rome.

At first glance, the argument that these suicides were moral seem simple enough: Unlike murderers, suicidal individuals cause direct harm to no one but themselves, and they do so willingly. In this view, the decision to die rather than to degrade oneself before an enemy might be seen as ennobling. However...