The fallacy for the idea that we put animals that are in irreversible out of their misery, so we should do the same for people is called "Faulty Analogy or Informal Fallacy."
Further Explanation:
This type of fallacy where the reader should put a person out of their misery like we do animals are wanting the reader to ignore how much of a difference there is between animals and humans. The profound differences are often overlooked by the ones using faulty analogy. A person would not be put down because they are ill because the differences in an animal and human.
Faulty analogy/Informal fallacy is when two things could be alike in some ways but far different in other ways. For example, someone could say "a person is immortal" is like "a car can run forever."
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