Tormentor
Akito's abusive relationship with Rin.
As head of the Sohma clan and the "God" of the juunishi, Akito is impossible to resist for those cursed with the spirits of the zodiac animals. When Akito learns that Rin and Hatsuharu have been dating, she confronts Rin alone and demands to know who's responsible for initiating the relationship. Rin is immediately intimidated by Akito's attitude and body language so she's reluctant to say anything at first. However, Akito reminds her of how she blinded Hatori in rage when he wanted to marry Kana. Afraid for Hatsuharu's safety, Rin lies and confesses it was her.
The moment that Akito hears what she wants to hear, the situation goes from bad to worse; Akito begins to physically assault Rin and when she sees Rin cowering, starts to tell Rin how disgusting and useless she is. Akito tells Rin her life is meaningless and that if she stays with Hatsuharu, she'll only bring him down with her. She then pushes Rin out of the window and Rin falls to the ground, two stories below.
Rin is hospitalized for several months, having suffered grievous wounds from falling out of the window. No one but Hiro knows exactly what happened so no one stands up to Akito for her behalf and Rin begins to actively avoid Akito. She's successful until Ren's mother tricks her into trespassing into Akito's room to steal a small box for her in exchange for learning how to break the curse. Akito catches her and in cold fury, throws Rin into solitary confinement for at least three months.
Rin's absence goes all but unnoticed until Kureno stumbles across her in the room by coincidence. Until then, however, Akito torments Rin. She brutally cuts chunks of Rin's hair off, strips her of her clothing in exchange for a plain yukata and threatens her that if she tries to leave, she'll hurt Hatsuharu. Akito knows exactly what Rin's weakness is and Rin eventually loses all will to live. She stops eating altogether and the only thing that keeps her going is a very infrequent dream of being with Haru in happier times.
Hatsuharu learns about the window incident and pays Akito a visit just after Rin is rescued. He demands to know where Rin is and what Akito has done to her. Akito begins to deny having any involvement in Rin's disappearance and even tries to manipulate the situation to make Haru the guilty party. When Kureno arrives mid-argument, he tells Haru that Akito had locked Rin away in the Cat's Room and Hatsuharu nearly pulverizes Akito's face in anger. Aside from Hatsuharu's rage and Kureno chastising Akito for her actions, Akito seems to go completely unpunished.
In the end, Akito realises the errors of her ways and allows the curse to break. She holds a banquet for everyone to reveal that she has been a woman the entire time and to formally apologise for all the terrible things she's done to them. While Akito truly wishes to atone for her actions, Rin is unable to accept any apology.
Analysis
My opinion on their relationship.
Although Akito has never been kind to the female members of the zodiac, she seems to have a hatred for Rin in particular. Akito's mother, Ren, is the reason why she hates women. Since both Rin and Ren share some similarities in appearance, Akito probably sees her mother in Rin. Akito is unable to take her frustrations out on Ren so it seems that she considers Rin to be a perfect substitute -- especially since Rin can't really fight back due to the curse that binds them together. We don't know if Rin tells Akito that she was doing Ren's bidding but if she did, this would certainly add fuel to the fire.Before her initial confrontation with Akito, Rin already suffered from neglect. She already believed that she was worthless and unlovable by everyone but Hatsuharu. When Akito tells her the same, it reinforces Rin's negative self-image. Akito also tells her that she will eventually crush Haru with the weight of her negativity. She already was concerned about this as well and hearing it from Akito in this situation really makes her believe it's true. As she lays bleeding on the ground after Akito's assault, she thinks that Haru would be better off without her. The best thing she believes she can do for him is try to free him from Akito's bonds so that he will never have to suffer in the same way she and some of the other juunishi have.
Rin tries so hard to break the curse so that Akito won't have control over Haru. This of course backfires and Akito confines her in the cat's room for three months, subjecting her to a tragic hair cut and all sorts of threats and emotional abuse. When Rin's freed of her confinement, she's a mess but she is able to piece together her life again thanks to Hatsuharu and Tohru's support.
When Akito has a sudden change of heart at the end of the series and decides to release everyone from the curse, Rin is the only one who seems unable to forgive Akito. She worries that this reflects poorly on herself but she can't come to understand why everyone can move on so easily. I personally feel that Rin is completely justified in thinking this way. She's been subject to so much torment and Akito goes completely unpunished for her transgressions. Akito tells Shigure that she doesn't know how she can apologise because she's done such terrible things but I don't think a simple apology can make up for Rin's pain.
I'm not sure if Rin will ever be able to forgive Akito but if Akito was truly sorry and really wanted to make amends, I can see Rin coming to a place far in the future where she's able to at least accept that Akito was also abused and maybe sympathise with her in some way. If this ever happened, it'd be years down the road.