The argument against life extension based on an appeal to nature states that it is wrong to extend life because it is not natural.

See for instance “Radical Life Extension Is Already Here, But We’re Doing it Wrong”:

But there is another, deeper argument against life extension—the argument from evolution. Its proponents suggest that we ought to avoid tinkering with any human trait borne of natural selection. Doing so, they argue, could have unforeseen consequences, especially given that natural selection has such a sterling engineering track record. If our bodies grow old and die, the thinking goes, then there must be a good reason, even if we don’t understand it yet.

External links

• Appeal to nature on Wikipedia
• “The Right and Wrong of Growing Old: Assessing the Argument from Evolution” (via the Atlantic article from above) argues against the appeal to nature