Garrosh is a deeper character than he gets credit for: Thrall is actually the one to blame for a lot of what Garrosh has done. Garrosh is trying to be like his father, but the problem is Thrall has only told Garrosh about one side of his father; the hero who died to save his people from a curse. He totally ignores the fact that while under the curse Grom was a bloodthirsty monster who wreaked havoc on the Alliance. So with all his war mongering, Garrosh is just trying to imitate his father, because he thinks that is how a hero and leader acts.