Alice has asked Bob to help her learn about a certain thing (for example, how to drive, since she's never bothered to learn). Or, maybe Bob has been assigned to act as a mentor of sorts at the workplace, since Alice is new there. However, rather than teach her properly, Bob decides to teach her all the wrong things. (This trope assumes that Bob is doing it on purpose; cases where Bob is making a sincere but incompetent effort don't count.)
The reasons for this vary. Perhaps Bob doesn't want Alice to pass her driving test; maybe he's afraid Alice will outshine him at work, so he tries to get her fired; perhaps Bob does this as a joke; or maybe Bob's just an asshole. Whatever happens, you can be sure hilarity will ensue.
This doesn't have to just be a tutor in the academic sense, but any time somebody is instructing another person in a subject.
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Anime and Manga
When Amelia asks Lina to teach her the Dragon Slave in a season one episode of Slayers, Lina deliberately puts her through a pointless Training from Hell that has absolutely nothing to do with magic in the hopes that Amelia will give up and go away.
This is a common plot device used in Naruto fanfiction. Naruto's lack of skills are often attributed to his teachers deliberately sabotaging his ninja training. This provides a convenient way for authors to explain his rapid growth in power once he begins learning things correctly.
In the First Try Series, Naruto and many other Academy students were sabotaged by Academy teachers as part of large-scale plan to weaken Konoha.
Guru of Dragon Ball Abridgedencourages Nail to stand up to Frieza by telling him that he's a champion of the old ways. After he leaves, Guru comments that if he'd taught him in the new ways, he might have stood a chance.
Dogtooth The father and mother of the main characters purposefully teaches them incorrect definitions to words in order to manipulate their world view and prevent them from ever learning certain concepts.
Harry Potter suspects Snape of this when Snape teaches him Occlumency. He was wrong: turns out Harry's just really bad at Occlumency.
Not that it makes Snape any less of a lousy teacher. The same applies to Potions, as Harry notes in the Half-Blood Prince that he finds Potions easier because Snape isn't shadowing over them like a bat, ready to bite their heads off at over all small mistakes while he's insulting them.
In Captain Corelli's Mandolin, Corelli wants to get on with the people whose village his men are occupying, so he asks an Italian-speaking local to teach him how to greet the villagers in their own language. The "greeting" he gets taught is thoroughly impolite, and causes him to become even less popular.
In Warrior Cats, Lionblaze claims that Ashfur (who has a grudge against Lionblaze's parents, as he was part of a Love Triangle involving them) has been teaching him to do everything the wrong way. Brambleclaw (Lionblaze's father), is shocked at the accusation because he knows it could possibly be true, but he also scolds Lionblaze for blaming others.
There's a whole series of humour books called "Great Lies To Tell Small Kids".
Live Action TV
In one episode of I Love Lucy, Lucy and Ethel wanted Fred and Ricky to teach them how to play golf so they could spend more time together as couples. The boys, not wanting their wives to intrude on their one activity away from home, teach the girls ridiculously made up and complicated golf rules in hopes of making them hate the game and leave them alone. When the girls find out, they get the last laugh by convincing a professional golfer to play with Fred and Ricky using the made-up rules, tricking the boys into thinking they'd been playing the game wrong this whole time.
In Grounded For Life, Sean deliberately "torpedoes" Lily when teaching her how to drive.
An indirect version of this occurs in the "Dirty Hungarian Phrasebook" sketch in Monty Python's Flying Circus. Someone deliberately publishes a book with wildly inappropriate English translations of Hungarian phrases to get the user in trouble. It's a trope namer for My Hovercraft Is Full of Eels.
Kelso:*faking a career day report* Autumn is harvest time for the farmer. At dawn, my dad and I were out in the fields, picking carrots fresh off the trees.
Hyde: Kelso, carrots don't... *Beat* That's good. You should write that down.
Frasier asks Lowell to translate a speech he wants to give his son at his Bar Mitzvah into Hebrew, but having failed to complete the favor Lowell asks in return, Lowell translates it into Klingon instead. Hilarity ensues.
Friends: Joey once taught a soap-opera acting class. One student asked Joey to coach him and prepare him for an audition for a role of a boxer that Joey wanted as well. Joey advised him to play the role "homosexually". It backfired, though, because it turned out that they loved it and the student got the role.
In one episode of Everybody Loves Raymond, Debra asks Marie to teach her how to make meatballs. Marie, fearing that losing her domestic edge on Debra will mean no one wants anything to do with her, switches the labels on the ingredients around.
In 30 Rock, it's revealed that Drew was taught absolutely everything that way. He was just too handsome for anyone to ever tell him when he was doing it wrong. As a result, he believes you can cook salmon in Gatorade.
On iCarly, Carly and Sam are dealing with the problem of tutoring a bratty kid. They teach him incorrect mathematics using nonexistent numbers, and he believes them and fails his class.
Extr@ always features Nic, a native speaker of the language the series is in, teaching Sam, an American with little knowledge of the foreign language, all the wrong words, e.g. teaching "basket" as "oven" so that Sam will shock everyone by saying "the dog is in the oven". Nic does this to make Sam seem stupid and prevent Sasha (who Nic has a crush on) from liking him.
On Family Matters, Steve Urkel once considered sabotaging someone in this way, because he saw the guy as a rival for Laura's affections. His better angels convinced him not to do it though.
Peanuts - After Linus was born, and he was still younger than the other characters, Lucy decided to take him under her wing and teach him Little Known Facts.
Lucy: This is an elm tree. Someday it will grow into a mighty oak. You can tell how old it is by counting the leaves.
A Running Gag on FoxTrot whenever Jason does anything related to tutoring. One of the few times he didn't do this was when Paige decided to pay Jason in function of her grade.
At least two times in Tank McNamara, a veteran football player is instructing a novice who's expected to replace him ... and advises the youngster to make a racist remark. "All the black defensive linemen think it's a barrel of laffs."
In Teenagers from Outer Space, human characters have the ability "Fake Out", representing their ability to convince an alien visitor of almost anything regarding Earth culture, customs, and what is cool, since after all a human would be an expert on the subject. (The attempt succeeds on a d6 roll of three or higher.) Teaching them wildly inappropriate things is the most common practice. (Although telling the hot alien babe you want to date that kissing is a standard form of casual greeting will backfire horribly.)
Played as a dramatic plot twist in Jade Empire. It is revealed that your master deliberately built in weaknesses into your fighting style, so that he could take you down after revealing that his name, Sun Li The Glorious Strategist was well-earned.
From the Street Fighter mythos: While training Dan, Gouken asks him his reason for taking up martial arts. When Dan tells him that it is so he can kill Sagat to avenge his father's death, Gouken lied and told him that his training is complete. Dan believes that there is nothing left for him to learn when in fact he is very lacking in technique.
Has been known to happen with American PO Ws during the Cold War being forced to teach enemy spies about how to pass as an American. For example, they might say to NVA agents that the Dead Man's Hand in poker is two pair, kings and jacks (it's aces and eights).
This is a common retaliation against bullies and cheaters on notalwayslearning.com. Hereareexamples.