We discover early that Plato suffers from some kind of emotional or behavioral problem when a detective asks him why he shot the puppies (0:08) and whether he ever talked to a psychiatrist (0:09). He answers with a question, "You mean a head shrinker?" And later (1:22) he answers the original question, "I went to a head shrinker."
We never meet either of Plato's parents, but we learn that they have abandoned him. On the other hand, we see repeated glimpses of emotional process in Jim's and Judy's families. Jim seems bothered by his perception that his mother and his paternal grandmother "make mush out of" his father (0:15), and he begs his father to "stand up" for him. What else could we hypothesize about the workings of either family?
Judy tell Jim she felt "numb" after Buzz dies accidentally while playing chicken with Jim. How likely is it that this symptom heralds Acute Stress Disorder? What about Plato and Jim? Would either qualify for a diagnosis? Might we better explain these cases in family systemic terms rather than in terms of individual pathology?
In the end, despite Jim's and Judy's heroic efforts, Plato dies after a trigger-happy cop shoots him unnecessarily.
References in Film Stars Don't Die in Liverpool, La La Land, Ode to My Father