Plato is extremely lonely. He has nobody in his life that really cares for him except the nanny that lives in the same house as him. His parents left him and did not even return to celebrate his birthday or Easter with him. He does not have any friends until Jim comes to his school.
Plato does not have parents that take care of him and love him. His parents are divorced and his mother went traveling leaving him alone with the house nanny. He really lacks a person to look up to and admire in his life so he sees Jim as a father figure. He really just needs somebody that he can look up to and know that they care for him the same way that he cares for them. He really sees a lot in Jim.
Plato is clearly not as stable mentally as I'm sure he would like to be. He really confides in Jim more than he probably should because Jim doesn't see him as a close friend the way Plato sees Jim. When Plato , Judy and Jim are in the mansion and Plato falls asleep Jim and Judy leave him. Plato wakes up when Buzz's friends come and terrorize him and he is really upset at Jim for leaving him alone. At the beginning of the movie Plato is in the police station for shooting puppies. He uses violence to help deal with his stress. When he leaves to go to the mansion he takes the gun with him from his mother's room. He needs something to protect him to feel safe.
The main problem Plato has is his family structure. His dad is never present and his mom is always away on trips leaving him alone. The lack of family and being cared about causes him to be really unstable as a person. He acts out in violent ways and that can really only be blamed on the way he was raised and the way his parents treated him.
The symbolism for Plato's socks being mismatched is that he was still very childish and in his extremely chaotic life the importance of his socks matching each other did not completely matter to him.
Does Plato Change?
Plato does not have any character growth compared to Judy and Jim. He is introduced inn the movie at the police station because he had shot puppies and at the end of the movie Plato was killed because he was shooting the gun he had taken from his house. Him not having any growth in the movie was the result of his death at the end.
I think that the theme of the movie was that dysfunctional families/parents really do have a huge impact on their children's lives. For example: Plato acted the way he did because he didn't have a loving and supporting family that he needed. His death was unfortunately the result of his dysfunctional family.
Does Jim Have Parental Problems Or Is He Just Spoiled Rotten?
I think that Jim has parental problems but his parents spoil him rotten hoping that it will fix the problems. It isn't uncommon for parents to do that. They sometimes think that their child will more respect them or care for them if they give their child whatever they want. Sometimes it works and other times it does not. In Jim's situation, his parents spoiling him does not help their family problems be resolved because Jim doesn't fall for their little game of giving him anything he wants.