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Black Cat (manga). Creed kills Saya because he thinks that she is holding Train back.
Yu-Gi-Oh!: This is how Dartz groomed each of his "Three Musketeers" to be vengeful bringers of the Apocalypse. It backfires on him when one of them discovers the truth about his tragic past, but Dartz has already acquired more than enough power to stop him.
In Battle Angel Alita, when Yasugun comes to his sensei to talk about fear of death, he is told that a perfect machine he is striving to be should feel no emotion and if its his sister that is the source of the doubt, he should kill her.
Naruto has a curious case: Sasuke's only goal from the beginning was to kill his brother, Itachi, to avenge his clan. As the series progressed he started to develop bonds with his teammates, only for the Sound Four to arrive and give him a beating and a Hannibal Lecture, to convince him that his bonds are holding him back and he should leave the Leaf Village to search for power.
In Kara no Kyoukai, Shirazumi Lio is convinced that the only thing holding Shiki back from a murderous existence is Mikiya, and attempts this along with Murder the Hypotenuse. Mikiya survives, but thinking he's died pushes Shiki enough that she eviscerates Lio, but she gets pulled back by Mikiya.
In the manga version of Whistle! Shigeki does this which can at times be connected to Friendly Enemy when When he defects to the other side and challenges Sho's team. This angers Mizuno in the process
In the comic book American Way the US government wants a college football coach to come back to work for them, training their super hero squad. The coach refuses for the sake of his wife, so the US government kills her so he'd come work for the gov't. Except it turns out they just gave her a million dollars to move to Wisconsin. Except not really, they did actually kill her.
Birds of Prey's David Cain once found two very promising martial arts-practicing sisters who he believed would be able to give him a suitable heir. Problem is, neither was dedicated enough to become that potential perfect mate. So he killed one of the twins and enraged the other to release the full power of her training as LadyShiva.
In the early issues of the new Batman and Robin series, Damian Wayne's mother Talia put control devices in his spine and manipulated his body in order to have him kill Batman (Dick Grayson). Her reasoning was that Dick was holding Damian back by making him Robin, though it was clearly more along the lines of unhappiness that Damian was not obeying her since when using the machine she even commented that "this is what it's like to have a son who does what I want." Damian refused her "help" after Dick freed him from the control, and his mother has since cut ties with him via Cloning Blues now that he's siding with his father's legacy.
This was somewhat the reason why the second Zoom attempted to kill Wally West's wife Linda (and succeeded in temporarily causing the deaths of their unborn children in Geoff Johns' Flash run. He felt that Wally needed a great personal tragedy in his life to strive to become a better hero, and Linda being alive in a happy relationship with him was preventing this from happening.
In Death Of The Family, The Joker is putting Batman and his allies through hell just to prove this point. He claims that Batman could be so much more than he is if the "Bat-family" weren't holding him back.
Daredevil: There was a period when the Kingpin had retired from crime at the request of his wife Vanessa; this galled one of the Kingpin's lieutenants. When Vanessa was kidnapped, during the rescue attempt the lieutenant attempted to kill her and blame it on the kidnappers (she survived, but nobody knew that until much, much later) so the Kingpin would return to his old ways. It worked perfectly...unfortunately, the Kingpin figured out what had happened, and the "old Kingpin" had no compunction about murdering a traitor with his bare hands.
In another storyline, Wilson Fisk moves to a different country and settles in to a humble life. He ends up falling in love with a local woman and becomes a father figure to her children. Then the Hand murders them all and shove a few swords into Fisk's back to get him back in the game along with a standing offer of leadership. Fisk takes the offer, but once again makes a point of killing the person who ordered the attack that killed his loved ones.
A popular trope within the Harry Potter fandom - the idea is that Evil Dumbledore has intentionally set things up to leave Harry with his abusive relatives and keep away anyone who might help him for the first eleven years of his life, to ensure that he gets an impulsive, angry hero who doesn't rely on adults.
In Harry Potter and the Methods of Rationality, Harry becomes briefly afraid that Dumbledore will dispose of his family once he realizes that they aren't abusive (and therefore might be holding him back) and thus pretends to be miserable.
In X-Men Origins: Wolverine, this is apparently why Victor kills Kayla. Only it turns out, it was Stryker's plan, not Victor's, and Kayla is not actually dead.
In Star Wars it is elaborated upon in the Expanded Universe that Palpatine had plans to kill off Padme anyway, he felt that Vader's love for her was holding him back.
This is very, very common in Sith training in general. Removing the "weakness of compassion" by killing a loved one is usually the last step in becoming truly devoted to the Dark Side. See Jacen Solo.
Despicable Me would have Dr. Nefario taking the orphans back to Miss Hattie because he thinks of them as distraction for Gru.
Speaking of the above, Megamind has this when Minion tries to stop him from dating Roxanne.
A less malignant version of this is what drives the main conflict of The Adjustment Bureau: the Bureau doesn't try to kill Elise but aims to keep her and David apart because David's drive to become a politician and make a positive difference in the world was his means to cope with the loneliness he felt after losing his parents at an early age (also due to the machinations of the Bureau). According to the Bureau, if David and Elise remain together, David won't become President and change the world for the better. Likewise, Elise would fail to become one of the greatest ballet dancers in the world.
In the French film With a Friend Like Harry..., Harry tries to clear all obstacles to his favorite writer's progress, including family.
This is what the villain of Decorator intends to do to Erast Fandorin in the end. Luckily, he fails.
The origin of one protagonist in Vladislav Krapivin's Crystal-verse series. One secret society is dedicated to protecting and teaching kids with unusual abilities, which Dark and Troubled Past makes more obvious, and they run a boarding school, so they only watch the bureaucracy of social services and push some levers... Either that, or find children they want to acquire, remove their parents making it look like an accident, then ride in on a white horse when bureaucrats "for some reason" deny custody to other relatives. Good news is that well intentioned extremists prefer "humane" methods of making people vanish: interspacial travel in the setting is anisotropic, so even if exiles know anything of this fringe discipline and somehow can make proper equipment in the world where they were dumped, good luck with finding a way back.
In Windmills of the Gods by Sidney Sheldon, the heroine turns down an offer from the President to become a US Ambassador. Unfortunately for her, the villain really wants her to take the job, so arranges for her husband to die in a tragic car crash, so that she will be free to accept.
Live Action TV
In Smallville, Jor-El does this to Clark, a lot. In Arrival, he tries to freeze Chloe to death because of this, leading to an extremely heartwarming moment.
Jor-El: Kal-El, you must continue your education. You cannot stop.
Clark: She is my friend. She needs help!
Jor-El: Your destiny is far greater than saving one human life.
Clark: No! I won't let her die!
He does it again, arguably worse, in a deleted scene between Blue and Persona. Jor-El intends to trap Clark in a crystal until all his loved ones have died so he won't be held back by anything, but luckily he has to release him to defeat Bizarro.
Earth: Final Conflict starts with this, when Boone's wife is killed by Sandoval. The killer does consider it a favour, too... then again, the killer committed their own spouse to an insane asylum so they wouldn't interfere with the killer's work for the Companions.
The ending of Harper's Island reveals that Henry is an example of the second variant. He brought Abby back to the island and started killing people with John Wakefield because he believes it's their destiny to live on the island together, with no one else. She doesn't take it well when she finds out.
Very narrowly averted in an episode of Burn Notice, in which Tom Strickler offers Westen a chance at his old life back, if he does some morally questionable jobs, which he eventually agrees to. Then Strickler kidnaps Fiona, who he claims is holding Michael back, and tries to give her to her enemies. Michael rescues her at the last minute, and shoots him.
In Nikita, Michael's wife and child are killed by a terrorist and Michael joins Division to enable him to track him down and exact revenge. only to find, of course, that the 'terrorist' was a Division agent and the killings done on the head of Division's orders, so that Michael would join them.
Another Star Wars example: In The Force Unleashed 2, Darth Vader tells Starkiller to give up on his love interest Juno because she is holding back his progress in the Dark Side, his exact words being, "Rise above this, she means nothing" and, "She was holding you back." Vader tells Starkiller this after Vader had just mortally wounded his girlfriend right in front of his eyes, and this does not bode well for Vader winning back his apprentice.
In God of War, this is Ares' rationale for tricking Kratos into murdering his wife and daughter. Naturally, this backfired.
In The Darkness, the titular creature prevents Jackie from saving his girlfriend, Jenny, claiming that she was a restriction on his personal freedoms.
The Darkness: She was a burden. This is freedom.
The sequel reveals that the Darkness was actually lying; as the vessel of the Angelus, Jenny was a serious threat, even if she didn't know it herself. So, the Darkness allowed her to die and captured her soul to prevent her from ever becoming dangerous- which backfires spectacularly when Jackie finds out and decides to free her.
In inFamous, Kessler killed Cole's future wife Trish because having a family will hold Cole back against the Beast in the future.
In strip #916 of The Order of the Stick, Tarquin believes Elan is being held back from becoming The Hero by following Roy's (the actual Hero of the story) lead. So Tarquin orders his entire army to kill everyone who is still in the crater (Roy, Vampire!Durkon, and Belkar).
In the last season of Codename: Kids Next Door, a mysterious splinter cell takes interest in Numbuh One. In one of the final episodes, they manipulate events so that Lizzie breaks up with him, breaking one of his last emotional ties before declaring that "He's almost ready".
In Young Justice, Harm did this to himselfmurdering his younger sister Greta, the only person he loved, so that he could become pure evil since the Sword of Beowulf will only bestow power on a "pure" individual. It ultimately failed; seeing Greta's ghost shatters Harm's "purity" and the Sword rejects him.