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I think the priests had some kind of a motive, political or otherwise, against the king, to put him in danger. Their method seems to be to get the king angry.
King Noah is also dependent upon his priests for counsel and suggestions, maybe even approval in some cases. He is the blood-related heir of the kingdom.
Let's examine some of the interactions between the two:
Mosiah 17:11-12 - the king believes the words of Abinadi, and was about to release him, but the priests got him angry again, specifically saying that he (Abinadi) has reviled the king – not the priests or the people.