He wanted to believe that her death was a natural one, as opposed to something violent or criminal.
He may have been socialized to believe that death is a natural part of life and that it is not something to be feared or investigated. He may also have been uncomfortable with the idea of a murder occurring in his neighborhood.
Additionally, he may have been afraid of the implications of someone in his community being capable of murder. It is also possible that Alan was in denial about the reality of the situation, and that his desire to believe that she died of old age was a way to cope with the tragedy.
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