If you think that's not the exact mentality underlying support for assisted suicide, you're either naive or in denial.
Okay, everyone is effectively terminal from the moment life is conceived, but to reduce euthanasia to your parameters is to miss the point. It's all very well to argue the analogy of talking someone down off a ledge, but supposing that person has only a week to live and that "life" is going to consist of horrendous suffering or being so out of it until they actually demise?
Does quality of life mean anything to you? Or should someone suffer until they naturally draw their last terminal breath? FTR I only support euthanasia with stringent and watertight safeguards for those who are terminally ill and do so with full cognitive ability.
And furthermore I would only have a pet of mine put down as a last resort, it certainly wouldn't be done out of "convenience"...
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