An argument, however sound, is not enough to dispel the fear of dying.

Objects to

Heidegger

The Epicurean argument treats the fear of death as an error of reasoning: whoever grasps that "death is nothing to us" should see it vanish of its own accord.
But this fear is not a mere opinion: it is the living being's attachment to its own existence, older than any reasoning and more obstinate than it. One can grant the conclusion and tremble still.
Experience confirms it: no one contemplates their own vanishing as a truth of geometry. What we dread is not a painful state, it is no longer being at all, and no demonstration has any hold on that vertigo.

Therefore So the promised serenity may be only a victory of words: reasoned sometimes leaves intact the very anguish it claims to cure.

Deepenings

Fear and anguish

One distinguishes fear, which always has an object one can face or flee, from anguish, which has none: before death, it is nothing definite that we fear, but the sheer "no longer being."
This is why an argument, which always addresses an object, misses anguish: it refutes a reason for fearing, where what would need calming is one's whole relation to oneself.

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