There are a lot of anime siblings with screwed up relationships out there. Some of these horrible anime brothers and sisters are trying to kill each other, some are trying to screw each other, and others come from horrendously dysfunctional anime families with terrible parents who make it pretty much impossible for their kids to get along. You'll find weird anime sibling relationships in everything from action hits Naruto and Kill la Kill to emotionally driven shows like Yuri!!! on Ice and March Comes In Like A Lion. Some of these messed up anime siblings could seriously use some family therapy.
Sasuke Uchiha's primary goal in life is to murder his older brother Itachi. He doesn't care if he dies, doesn't care if he has to mortgage his body to the deplorably creepy Orochimaru, doesn't care if he has to kill hundreds of other people and betray his friends, he only wants to end his brother's life. Why is this so important to him? Because Itachi murdered all the rest of the Uchiha clan, leaving Sasuke an orphan.
This is screwed up enough, before you start layering on the complications. First of all, Sasuke adored his brother prior to the event, so the betrayal hits a lot harder than it might have if they weren't close. Second of all, Itachi had little choice in the matter. At age 13, he was convinced by a corrupt government leader named Danzo to take out his whole family. Why does he agree? Because if he doesn't, Danzo would have the whole family killed anyway. By killing his family, he was allowed to spare his own life, and that of his baby brother Sasuke. Had Itachi told his family and tried to fight back, it would have sparked a civil war, an option that a teenager with war-induced PSTD isn't likely to go for.
Sasuke doesn't learn any of this until after he gets his revenge, so the two never have a chance to reconcile. Thanks for the heaping helping of tragedy, Kishimoto.
Mitsuki and Yuuya Kanzaki are step-siblings. Before we go any further, please realize that this doesn't make them not siblings. Anime likes to use step-siblings to make incest seem less icky, but anyone who's been part of a blended family knows that's bullsh*t.
Anyway, Yuuya's friend Hiyori was madly in love with him before she died. Now, those feelings are keeping her ghost from ascending to heaven. She solves the problem by possessing Mitsuki, Yuuya's sister, and tries to consummate the relationship using her body. This totally ruins any chance the siblings might have had at a normal brother-sister dynamic.
Although their relationship does improve somewhat over the course of the series, Inuyasha and his half-brother Sesshoumaru pretty much hate each other. Why? Because Inuyasha is half-demon, half-human, and Sesshoumaru, a demon without the human influence, has a huge problem with that. Basically, his issue is fantasy-world racism. That, and the fact that their demon father gave Inuyasha the Tessaiga, a weapon far more powerful than the Tensaiga he gave Sesshoumaru.
At one point, their relationship gets so bad Inuyasha chops Sesshoumaru's arm off. Obviously, it's not exactly loving.
Watamote, also known as No Matter How I Look At It, It's You Guys Fault I'm Not Popular!, focuses on a high school girl named Tomoko Kuroki whose social skills are, shall we say, lacking. She desperately wants to make friends, get a boyfriend, and be popular, but she has no idea how to go about it. She enlists her younger brother Tomoki to help her out, which could be heartwarming, if she weren't asking things like "Can I see your penis?"
Needless to say, Tomoki isn't particularly fond of his creepy older sister. Most of their interactions involve him screaming at her to leave him alone, insulting her, or throwing her out of his room. Moments of kindness between the two are often laced with ulterior motives. For example, Tomoko tries to "take care of" Tomoki when he's sick, but actually just wants to catch his cold so that she can get out of school. With aggressive screaming from Tomoki and awkwardly sexual overtures from Tomoko, the relationship between the Kuroki siblings just plain sucks.