7 Now this he did that he might preserve their hatred towards the Nephites, that he might bring them into subjection to the accomplishment of his designs.
8 For behold, his designs were to stir up the Lamanites to anger against the Nephites; this he did that he might usurp great power over them, and also that he might gain power over the Nephites by bringing them into bondage.

Zerahemnah follows the example of despots and tyrants throughout the centuries. He sought power and control over his people and a way to subjegate others as well.

To do so, he sought to scapegoat and generate hatred. And in doing so, his most powerful weapon are the Amalkeites and the Zoramites who were once Nephites themselves. This former members of the Nephite nation likely spread their narrative of Nephite oppression and persecution. And this coincided well with dormant hatred that had long existed among the Lamanites. Many likely also felt that the Nephites has corrupted their brethren by converting them
All of these animosities converged into a desire to take over the land of the Nephites and to stop their worship.