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What is ''immoral'' is subjective to each individual and what belief system they hold.
Your argument is not sane in a general sense. A proper formulation would be it is not NECESSARILY immoral to take a life, which I agree with. You cannot make the general affirmation of your original argument.
A far better argument would be "not inherently immoral". As is, not only is morality entirely subjective, but you can easily point to examples where most would agree the taking of a life was immoral.
To condone the killing of a human being, one would need to operate under the assumption that the person's life is not their own. This assumption is problematic, as it leads towards an endless cycle of killing, as well as slavery and basically every other evil that one person can inflict on another.
Because "the taking of a life" is an action and "immoral" is not an action. Hence they are not the same.
If every human was polled "Is the taking of a life immoral?", almost all of them would say that it is immoral.
Argumentum ad populum chiron
This claim is purely based off of assumption, along with the consideration that even if such a poll was conducted with the predicted results, a large group that has reached consensus does not mean the answer agreed upon is correct. 6matthew12
Humans are programed to want to forward the species, not the opposite. Therefore, it is immoral to kill because it is the opposite of human nature.