When the initial leap happened it was established that Arohi was obnoxious but still very close to her sister (when they were 8-9). She was competitive but she and Akshara got along just fine. Then they found out Akshara wasn't Sirat's daughter and Arohi's first reaction was well what does it matter? Akshu's crying for nothing. Our father's still the same. Then a series of events happened simultaneously. She saw Sirat hugging Akshu and telling her how she's more x than Arohi and her favorite. (It's been some time since I saw this scene so cannot confirm the dialogues for sure but Sirat's said something that made Arohi feel like she was giving Akshu preference over her).
Then Manish did the same and Arohi overheard. Then she met her maternal grandmom who'd been insulted and ousted from the Goenka house and she filled Arohi's ears with how she'll always be secretly loathed like her and how Akshara will always be preferred over her because Akshara's royalty -- Naira's beti. That set a subconscious shift in Arohi's thinking patterns.
Then Arohi grew even more possessive of Sirat. It's here she started hating Akshara for being who she was -- an empath. It was established that Arohi was 'mu-phat' or 'outspoken' and so obviously she must have been reprimanded quite often. Akshara on the other hand was the quintessential good kid who did everything right. It's possible, and most likely, that Arohi began to hate her for these very qualities as Arohi's personality was being compared to her Nani who was considered inferior and evil by the Goenkas (the woman was a piece of work but Arohi didn't know that).
Kartik was away and they all believed the moment he returns he'll sort this out between the girls because 'only' he could handle them and set this straight. But Kartik died in a plane crash before returning home.
Arohi had already started taking subtle digs at Akshara by this point. She didn't fully hate her but I think once that subtle subconscious shift happens everything the other person does somehow becomes evidence aiding the hypothesis you've constructed in your head. Cognitive bias.
Akshara was told point-blank by Manish and others that she was their favorite. I think Surekha was covertly hostile to Sirat and she made quite a few remarks about Arohi taking after her Nani. Both Akshara and Arohi noticed these things. Arohi even noticed her mom being reprimanded by Manish and didn't take it lightly.
All of this just added to Akshara's guilt. Every time Arohi acted out Sirat told Akshara that she was 'na-samajh' and Akshara was mature and she needed to forgive Arohi. Then Sirat died and Arohi blamed her. So, yes there's a lot of conditioning here. Akshara still thinks Arohi is 'na-samajh'. She's an empath and so every time Arohi blames her for getting preferential treatment I think Akshara acknowledges there's a smidgen of truth to it even if that's not the case anymore. She sees it as her responsibility to help Arohi find happiness and stability because 1) this was Sirat's dying wish and 2) because she knows Arohi is hurting and burning up inside.
And the icing on the cake -- Akshu's basic mental model -- is to put family above everything else. So to her there's no cutting off Arohi from her life. Forgiveness comes easy to her and the guilt she's racked up over all these years drives her relationship with Arohi.
Obviously, her mental models are toxic and unsustainable but this is ITV so IDK how this is going to be dealt with.
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