Homers relationship with Bart and the other children is very dysfunctional to say the least. His interactions with his son most often consist of a highly angered reaction to something that Bart has done at which point Homer lashes out, strangling Bart. According to Horney, when children experience a lack of affection from their parents this can lead to future feelings of isolation. The anxiety that stems from these feelings effect ones interactions with other people; whether the are withdrawn, move toward, or move against others.
We can see from Barts interactions with others on the show that he is actively moving against others. His behavior is often defiant and he strives to master every situation he finds himself in. As he exploits the weaknesses of others to gain respect and attention, he is working to relieve the feelings of basic anxiety that stem from his realtionship with his father.
Bart has two true friends, Milhouse and Ralph Wiggum, both of whom are outcasts socially and look to Bart as a leader. These types of relationships, according to Horneyian theory, satisfy Barts neurotic need for power and exploit as well as his neurotic need for personal admiration. As Barts interpersonal relationships have been effected by his relationship with his father, so too has his perception of himself.
Horney believed that basic anxiety can also have intrapsychic consequences as well. Barts earlier conflicts with his father could effect his journey towards self-realization and result in an idealized self-image and a neurotic search for glory. That Bart has an idealized self-image is apparent from his behavior an can be observed as he acts out against authority as if there are no consequences for his actions. His belief that he is in control of every situation is an example of the neurotic perception of his own exalted faculties. Barts relationship with his father, following Horneyian Psychoanalytic Social Theory, would greatly impact his personality development. To anyone who has seen The Simpsons, it is obvious that Barts anti-social behavior is a product of his dysfunctional family life and specifically, his realtionship with his father.