Kate Keller is a controlling person for whom family is very important. Because Larry's body has never been found, she refuses to believe he has been killed, though the rest of the family is ready to accept this reality. As it becomes more and more obvious, even to Kate on a subconscious level, that Larry is never coming home again, Kate becomes more and more insistent that Larry is alive. In act 1, for instance, she says, in reference to Larry,
Certain things can never happen.
Later, in act 2, she states,
God does not let a son be killed by his father.
This latter statement points to the connection Kate knows exists between Larry's death and Joe's guilt in sending out the cracked airplane cylinders that caused twenty-one young pilots to die. If Larry really committed suicide because of his father's act, this means that Joe really did something wrong. Given how wedded Kate is to materialism and her husband having done the right thing in protecting his job and the family income, not admitting to Larry's death becomes psychologically central to her maintaining a worldview that upholds Joe's essential goodness.
The effect of Kate's denial is to hold the family in stasis so that they cannot move on with their lives. For example, Chris can't get engaged to and marry Ann if Larry is alive, because in that case, she is Larry's girlfriend. He can't progress in this situation, nor can Ann.
Kate goes to lengths to deny Larry's death, even to the point of confusing memories with reality. Kate uses Ann's memories as evidence that Ann thinks he is still alive, while Ann argues, "How could I help remembering him?"
Ann finally, in act 3, shows Kate the letter in which Larry says he will kill himself. Ann knows that Kate has to enter reality for the family to begin healing and moving forward.