The first argument was removed. An appeal to a dictionary or a definition does not make it right or justified in its position. However, it may be speculated or conceived that it is not murder because the premeditated advancement of death by a person of another has been consented to in principle thereby the choice being made is a deliberate one for which one's right in its very own nature permits the condition to be moral.
Secondly for describing euthansia the Germans use the term Sterbehilfe which means "help to die" so while the person and maybe society may be complicit in the "killing of a person" they are accessories and not the actual agents of the killing as they are helping a person to die rather than determining that a person should die, something that would be viewed as murder [[Collins lanugage dictionary]] .