Self-murder ist m.E. ein Wort, das -wie schon von anderen gesagt- keineswegs ein schlichtes Synonym zu suicide ist.
But murder is defined as “the unlawful killing of one human by another, especially with premeditated malice.” So, as any intelligent person can see, suicide unquestionably DOES NOT fit the definition for murder…at all.
The first problem with labeling suicide as “self-murder” is that it implies suicide is a crime. But suicide is NOT a crime. People who die by suicide are trying to stop their pain. There is NO criminal component to suicide. Period.
Next, the word “murder” implies a very evil intent to bring the most severe harm imaginable upon another person. But with suicide there is NO evil intent and NO desire to bring harm upon another person. Again, people who die by suicide want to stop their pain.
And “murder” means the killing of another person. But there is no other person killed in a suicide.