As long as euthanasia is subject to stringent checks and balances to ensure it really is the individual's choice, it should be available to them. There's no murder involved if the person requests to end their life with full decision making facilities - as Papewaio notes, we extend this courtesy to the suffering animal all the time.
I believe that the means for dignified suicide should also be easily available. If I so wish, I can end my life quickly but messily (and traumatically for relatives and staff) with my shotgun. If I were minded to, it should be available to me to go to a doctor and request the necessary drugs to end life gently, and to arrange the going to my taste - without harassment from law or moralists - and with proper arrangements so that my family don't have to deal with such distractions.
Of course, it would be the right of medical personnel who do have objections, religious or otherwise, to refer on to someone else, but the principle would be one of my choice.
Once again, the only reason these choices are not available to us is the lingering impact of religious dogma. There is such a thing as the sanctity of life, but not because that life belongs to some Creator God. That life belongs to me, and I should have the choice as to how I end it, just as I have the choice of how to live it.
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