Described in "Officer Krupke" in West Side Story, where the Jets sing a mocking song to a (not present) police officer describing various excuses for their misbehavior.
My Daddy beats my Mommy, my Mommy clobbers me,
My Grandpa is a commie, my Grandma pushes "tea",
My sister wears a mustache, my brother wears a dress,
Gloriosky! That's why I'm a mess!
At a later point the Jets claim to just be work-shy, shifty punks.
Dear kindly social worker, they tell me get a job
like be a soda jerker, which means I'd be a slob!
It's not I'm anti-social, I'm only anti-work
Goodness gracious! That's why I'm a jerk!
Ultimately subverted. At the end of the song, the "authority figures" (actually the Jets themselves) do a quick rundown, before finally concluding that the real problem is Krupke, and if he'd just leave them alone, everything would be fine. Of course, the whole point of the song is to show one of the members how to "game" the system by feeding whomever he's talking to at the moment whatever line they want to hear.
Joseph Pitt from Angels in America had a rough relationship with his now-gone father. During a phone conversation with his mother, he asks if his father ever loved him. She dodges the question. When he tells her that he's gay, she snaps that he knows damn well his father never loved him, and that's no excuse for him to be acting up like this.
Later on, discussing her son's homosexuality with his wife, she says "...they think it's mothers who are close to their sons that cause this. Well, guess we disproved that theory, he and I."
Pity the child who has ambition Knows what he wants to do Knows that he'll never fit the system Others expect him to Pity the child who knew his parents Saw their faults, saw their love die before his eyes Pity a child that wise
In the Swedish version of the show, Molokov gets "Glöm Mig Om Du Kan" (roughly translated to "Forget Me If You Can"), where it's revealed his devotion to the Russian Revolution caused his lover Natasha to leave him. As such, his believe in sacrifice for the greater good motivates his manipulations throughout the show.
The actor playing Cox in the stage version of Nation decided to give his character one of these (dead wife and son), as his diary exercise for the character reveals (on page 22).
In All Shook Up Matilda has one for the way she acts as mayor.
In Chicago, Roxie Hart sings a line in the song "Roxie" that goes "And the audience loves me. And I love them. And they love me for loving them, And I love them for loving me. And we love each other. That's because none of us got enough love in our childhoods."
The trope namer is Freud's essay "Character Types Encountered in Psychoanalytic Work," in which he argues that we sympathize with the Duke of Gloucester in Shakespeare's Richard III because, in the play's opening monologue, he explains that he is evil because he is ugly: "What he is saying is: Nature has committed a grave injustice in denying me the comeliness of form that wins the love of others. Life owes me some compensation and I shall have it."
In How I Learned to DriveLil Bit comes to the conclusion that her abusive Uncle Peck was abused as well "Now that I'm old enough, there are some questions I would have liked to have asked him. Who did it to you, Uncle Peck? How old were you? Were you eleven?"
Bradley and Tilden were abused by their parents in Buried Child, leading to Bradley's aggressive nature and Tilden's dissociation.
In Pokémon: The Mew-sical, Giovanni's mother killed his pet Pikachu, prompting him to capture Ash's, as he wants to believe it's his old Pikachu.
Farquaad: No father of mine would've abandoned me in the woods as a child! Farquaad's Father:Abandoned you?! You were twenty-eight! And living in my basement!
In this case it's the hero rather than the villain, but the titular protagonist of the Mrs Hawking play series has harbored bitter resentment towards her father ever since, after ignoring her for most of her life, he forced her to get married whether she wanted to or not. It was a major contributing factor in her present-day inability to trust men.
In the musical adaptation of The Toxic Avenger, the town bullies Bozo and Sluggo give excuses for their bullying during the song "Get the Geek".