euthinization (probly spelled wrong)

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If murder is a sin, why is it ok to euthinize your pets? I think its a good thing to alleviate the animals suffering if they are dying anyway. Why isn't it ok to euthinize a person that's dying and suffering? If I were dying of lets say cancer and was in the final stages where i was suffering, in horrible pain that drugs may not help and i knew i was going to die very soon why couldn't i make the decision for someone to kill me or for me to take my own life? I do not believe in suicide but why is it different then "putting your pet to sleep" in this situation?