User blog comment:IE2555/A discovery on the Official Website.../@comment-1272757-20140212222901

Ryze and Brand's are enemies most likely for the same reasons Ryze has animosity towards Xerath. Brand uses magic (or at least wants to use it) to completely destroy or "cleanse" the world. Ryze has very strong beliefs about using dangerous or powerful magic irresponsibly; his "inspection" or whatever it's called revealed that he betrayed his mentor and possible lover to steal the scroll he currently carries, to keep the dangerous magic inscribed on it from people who would misuse it. So naturally, he would have animosity towards someone who wants to use magic for planet-wide destruction.