"That people die" is not "part of human nature" in the sense intended by that quote, which means something like "how people think and react".
"How people think and react" was Anissimov's subject of the moment. Many things, including both that one and human mortality, have been asserted to be "part of human nature". Look up anyone arguing against life extension. It won't take long to find the argument that "mortality is part of human nature". Literally. It took me less than one minute to find this:
The US President's Council on Bioethics claims that the human life cycle has an inherent worth and that, consequently, age-extension technologies distort or pervert the ‘natural' or ‘proper' human lifespan (President's Council on Bioethics, 2003).
The original source of what is there paraphrased is here (PDF, see pp.189-190).
Furthermore, you can't actually put any assertion you like in that template because the template only works with true assertions.
It works -- that is, can be sincerely said -- for anything the writer believes. It shares this attribute with bald assertion, but surrounds the assertion with an applause light frame.
"X is part of human nature" can mean
-- X cannot be changed
-- X should not be changed
-- X has particularly deep connections to human psychology
"How men and women are attracted is part of human nature" normally has the third meaning. "Death is part of human nature" normally has the first meaning, and so isn't comparable. In your quote, "death is part of human nature" has the second meaning; that is indeed a fallacy, but has no bearing on the original statement since that doesn't use the same meaning.
...It works -- that
Another month, another rationality quotes thread. The rules are: