Biography
Parents are supposed to be the protectors of children, but these parents are either so damaged themselves that they can't do the job, greedy or villainous to the point that they never had any interest in doing the job properly, or would rather use the child as a means to an end. Sometimes they're just sadistic assholes.
This includes parents who are emotionally, verbally, physically, or mentally abusive, or who neglectfully allow their children to be abused by others if they don't abuse the child themselves; sexual abuse in particular is typically treated as a special kind of evil. Sometimes, the abuse at the hands of their parents becomes a Freudian Excuse for a villain. Other times, the character manages to not grow up broken, bitter, and hateful, and instead a different and better person than the upbringing would incline one to think; they may even pass down their newfound betterment to their own children. Troubling Unchildlike Behavior is often a tell-tale sign that things are not right at home.
Abusive Parents are commonplace in fairy tales and Classical Mythology which makes this trope Older Than Feudalism. Note that The Brothers Grimm, when they collected European fairy tales, were uncomfortable with the idea of Abusive Parents and so frequently changed the Abusive Parents in the traditional stories into abusive step parents.
Sometimes, a parent will go as far as to kill the child in question, in which case this is Offing the Offspring. In other ways cases, the parent's abuse occasionally drives the offspring to snap, commit Revenge and finally kill them, thus becoming a Self-Made Orphan. Although other times, the parents end up as a Karma Houdini. Calling the Old Man Out occurs when a fed-up child retaliates with a "The Reason You Suck" Speech. If the child gets out of the broken family and forms healthy friendships, but reacts badly when their abusive parents show up again, well, Friends Are Chosen, Family Aren't.
Bear in mind that not everyone agrees on the line between actual abuse and merely heavy-handed parenting (or even normal parenting). Is Moving the Goalposts merely inspiring the child to achieve more, or the most insidious form of abuse to instill mistrust and paranoia in the children? Some include spanking as abuse; others think it's appropriate given certain guidelines. Some believe it's okay to make a kid go without a meal (they won't starve that easily); others disagree. Making a kid miss a friend's birthday sleepover — is that emotional abuse? Raising a kid without exposure to TV? Telling your daughter she's getting fat? A little name-calling? There's a line here somewhere, but not everyone agrees on where it is.note
If a parent has just dumped the child, for whatever reason, that's Parental Abandonment; if they aren't paying attention, that's Parental Neglect. If the parents refuse to discipline their kids, they are Pushover Parents. Contrast Mama Bear or Papa Wolf (where others abuse the children and the parents abuse the abusers), and the more extreme variant of Knight Templar Parent, where the abusive parent is violently overprotective. Also contrast Abusive Offspring, where the children are abusive to their parents. Abusive Precursors can be considered this, on a metaphorical level. See Hilariously Abusive Childhood for when this is cranked up to absurd levels and Played for Laughs. Black Comedy is often connected in the comedic aspect of it, and a Big, Screwed-Up Family may be involved if it is adult comedy. In keeping with the above note, some may call the show on it and say Dude, Not Funny!. See Evil Matriarch and Archnemesis Dad for characters who are beyond abusive and outright evil. Abusive-type parents are mostly wanted criminals being chased by the law. For grandparents who abuse their grandchildren, see Gruesome Grandparent.
While they do not have to be the child's actual, technical parents to be part of this trope, they must be closely related and live together, like a Wicked Stepmother or an Evil Uncle taking care of the Parentally Deprived. After all, it's much more disgusting that somebody related to the child could bring themselves to hurt them, rather than a mere foster family.
As in Real Life, this trope can make a child Hate Their Parent.
When the abused child in question grows up and starts their own family, they will sometimes bow not to make the same mistakes their parents did with them and will try to treat their own children better with the hopes of Breaking the Cycle of Bad Parenting.
The polar opposite, of course, is Good Parents.
Unfortunately, Abusive Parents are Truth in Television and a very sensitive topic for many, so No Real Life Examples, Please! - It is sufficient to say they do exist and that they are also Too Common.
Note: Please do not use this trope for complaining about parents you don't like.