Quote from Aseeker
this is just my 2 cents on this.
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kaname was adopted to the kuran family. rido (the uncle) probably was against that. yuki's parents probably picked him (kaname) up from somewhere and treated him like their own child but they also want him to be the successor so that their real child (yuki) would not be burdened with the responsibilities and danger that awaits her if there was any, like rido (the uncle) plotting to overthrow his younger brother (haruka) by killing yuki but has now changed or probably changing his plans by making yuki his bride (which is sick) maybe because his fiancee (shizuka) is dead. Yuki is definitely the key to all this. Her blood is probably something "special", like it could calm or soothe a vampire's lust for blood or something which would mean she can be a mediator for the vampires and humans. Because maybe her parents are just kind vampires who just wants to live in harmony with humans because they did contribute to the peace treaty.
Another note.
i dont know if Kaname loves her as a man but i know he loves her as an older brother that would protect her little sister would coz he did say he wished he was her "real older brother". He probably loves her so much because she was kind to him and accepted him when he came to the family. Yuki is probably mixing her feelings of love with sisterly love for kaname which she forgot coz she did lose her memories. thats why she so attached to him. But if this does turn out to be incest, that's fine too. it adds flavor to the manga. hehe. but other people probably dont like it. even if they're not related by blood but if you're taken in, that makes you family. people probably have different interpretations to incest.
And why she said sorry? i could only guess that yuki loves zero but she made the deal to become kaname's lover so that she could know her past or something like that.
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I really think Yuki is the one adopted in the Kuran family not Kaname. Just because of something Rido said in the chap. "I see you couldn't use my blood could you?" "Well that's ok..which ever way it happens, that girl will have Kuran's blood in her, which is ok" Now if Kaname was adopted in the family, he wouldn't have Kuran blood. But I do agree with maybe Rido wanted Yuki as wife because her blood and herself is special in some way, and that Yuki is sorry for putting Zero into all of this cause she deeply cares for him( maybe love, i think she's still confused to really tell)