Homicide is murder and is therefor a sin. Suicide is also murder and also a sin
Nope; if this were true then there would never be a justifiable homicide, yet there are — even in the Old Testament Mosaic law.
(Ex: Ex 22:2 If a thief is found breaking in, and is beaten to death, no bloodguilt is incurred;.)
Suicide is also murder and also a sin
If that is the case, then Jesus [who intentionally ended his own life (therefore committing suicide)] sinned; we know this to be false.
This raises a contradiction, therefore one or more of the predicates must be false.
the intentional taking of one's own life.