At least to my colonial ear, "suicide" sounds considerably more gentle than "self-murder." (And this is evidently a distinction that matters to people who think a lot about such things: Suicide is NOT Self-Murder - Suicide.org! )
I've never heard the expression 'self-murder' before! It is quite funny. :lol: This expression would only be used self-consciously or for comic effect surely. Just use 'suicide' - the proper word for killing yourself. To say 'he committed suicide' is perfectly polite, proper English.
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