@vivify saidWhen I go out on my motorbike I don't drive in a reckless and dangerous way because of my natural fear of death.
Living things are wired to be afraid of death, just like they're wired to reproduce. Fear of death is an instinct that helps keep a species around to continue evolving.
If I were to kill myself that way, it wouldn't have been inevitable.
The "anxiety about death" being referred to here relates to coming to terms with one's inevitable death at the end of a finite existence.
Two different kinds of death with different philosophical implications.