This can be occasional Truth in Television (with exceptions of course), with many cases in criminal psychology finding a link between anti-social behavior and a history of child abuse/neglect, but Sigmund Freud was mostly Right for the Wrong Reasons (he pinned this on hysteria and sexual repression problems), and this can actually be explained by modern concepts such as Social Learning Theory. Children are actually more likely to do (and exaggerate) behaviors if other people did them, especially when behavior comes with appealing rewards, and even if said behavior is bad/violent and the very people who are doing it do try to convince them to never do said violent behavior (how actions speak louder than words is hence why children are susceptible to Do Not Do This Cool Thing). For example, if someone was abused by their parents, they will be more likely to abuse their own children, because they will see it as normal (or at least justifiable) behavior.
In behavioral psychology/operant conditioning, the child's bad behavior can be amplified by receiving constant punishment, discouragement, bullying, manipulation, and abuse for good, altruistic behavior (e.g., Turn the Other Cheek in childhood only gets disproven as wide-eyed idealism), and how the child observes bad people surviving and even getting rewards for arbitrary violence (like said abuse). Ergo, it becomes reasonable to dispose of altruism and adopt ruthlessness for the sake of survival, self-improvement, and other such incentives. This conditioning is particularly devastating in childhood since children, without an inherent moral code, need outside reinforcement and role models to develop ethical behavior and Social Skills. In this case, a Freudian Excuse would have more impact if coupled with Adults Are Useless, which gives the child a jaded perception that the adult law is useless in general.
In Psi-Theory, constant abuse in childhood can lead to a persistent feeling of incompetence. Strategies to resolve this feeling, among others, can include the accumulation of political power, the accumulation of wealth, or violence towards weaker persons. Sometimes, in more neurologically based cases, the "Freudian Excuse" can be caused by mere brain damage, neglected brain development, or a persistent "fight-or-flight" response state which was the result of said abuse. Whatever the reasons, this trope is often brought up in Real Life discussions as a form of insanity defense and/or a reason to ban corporal punishment.