So he's been detained, handcuffed, had his phone with evidence of a crime on it seized, been driven to the police station and is being questioned about his son's death by a suspicious Stoddstd, and he decides to make LE's job easier by offering up, unilaterally, the beginning of his premeditated plan to murder his son?
That would be keeping in the personality that Leanna, friends, and family have testified to. The part of his personality they claimed to know well, at least. IMO