Why does it take so long for Ivan’s family to come to terms with the fact that he is dying?
The reason has to do with the way that the family interacts with each other and how they are not emotional. They are distant and formal with each other. This is how Ivan Ilych has lived all his life, separate and emotionless from his family. The only thing that matters to him is how he looks socially, is he respectable, do people believe that he has money and is a respectable member of society. Can he get invited to the best parties, do upper class people want to associate with him?
He does not really care about people, just about social status and possessions. So his family, including his wife, daughter and son behave the same way, even though he is dying. They ignore the obvious, as Ilych lies in his deathbed, they continue to attend social events, especially when the daughter gets engaged to a wealthy young man.
It is only his son, Vladimir, who is not really like the rest of the family, but more like the peasant Gerasim, who expresses love and sadness over his father's impending death. His son, as Ivan Ilych is about to die, kisses his father's hand and shows his sorrow.