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It's because Thor won't take his father's throne that Balder is forced to. As Karnilla points out, though, it's really Thor's fault that they have to be separated. So despite the love that they both profess for each other, they are forced to separate.
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Karnilla had already agreed to devote herself to trying to find a way to restore her people, and thanks to the growth of her character in this story, she doesn't hide the note from Balder when they arrive back in her kingdom. While Balder is rescuing Karnilla, Hogun of the Warriors Three arrives in the Norn kingdom and leaves a note saying that Balder has to return to Asgard and take the throne.
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But as White Pepper notes in the comments, that scene was told from Agnar's perspective, and we learn the truth here. One of her goblin servants seemed to betray Balder during his quest to save her, and Balder seemingly tricked him into getting killed. He's also somewhat deceptive to Karnilla.
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