A small boy laughs and copies his father's cough, not understanding that the sound belongs to a terminal illness. The poem sets that innocent game against a grim fact: the father is expected to die within a month. The mother tries to stop the child, and the father objects. Then he walks out, hoping to make her feel guilty for letting it happen.
The speaker stays quiet and describes the scene without comment, and that restraint is what gives the poem its force. We aren't told what anyone feels. We have to read it in the actions: the toddler's cheerful smiling, the father's anger, the wife caught between them. The father's reaction looks like grief and fear turned into blame, aimed at the person closest to him. The title is ambiguous too. "Letting this happen" could point to the cough being copied, but it also hints at the larger thing nobody can prevent. The mood is uneasy and sad, with a bitter edge, because the child's cheerfulness makes the loss feel even closer.