According to "The Death of Ivan Ilyich," why is it important to acknowledge one's own mortality?

I think the easiest way to answer this excellent question
is through an analysis of the final section of this tremendous short story. Throughout
the majority of this tale, Ilyich shows that he is incapable of accepting the finality
and inevitability of his own death, which of course is something that parallels the
insignificance and pointlessness of his own life and of those around him, most
particularly his wife and colleagues. His wife in particular keeps up her rigid social
demeanour in the face of her husband's death and treats it as something bordering on an
annoyance or an unwelcome distraction.

However, in the
final section of this story, Ilyich is able to acknowledge and accept his death, which
gives him a moment of epiphany when he is able to see how he has lived his life without
any compassion. When he understands this and accepts this, he is able to express his
pity and love towards his wife and son, and his fear of death is eradicated in the light
of this new self-understanding:

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And suddenly it grew clear to him that what had
been oppressing him and would not leave him was all dropping away at once from two
sides, from ten sides, and from all sides. He was sorry for them, he must act so as not
to hurt them: release them and free himself from these
sufferings.

Recognising and
accepting our own mortality is thus vital for us to understand ourselves and to look
upon our lives and how we have lived them accurately. Only by doing this was Ilyich able
to understand himself and show love to those around him.