Though he might never admit it out loud to anyone, Riku had originally been annoyed with Kairi from the very beginning. While Kairi had proved to him that there were other worlds out there other than his own, he did not approve of the fact how everyone on the Islands had quickly accepted her without any qualms or suspicions. Being the practical one, Riku had made sure to stay away from her, almost thinking of her as an 'alien' of sorts.
He was even more enraged at the fact that Sora had befriended her and had brought her into their private cave. Riku distinctly remembers how livid he had become when he had seen drawings other than his and Sora's drawn on the craggy rocks. To him, that place had become a symbol of his and Sora's trust; that anything and everything that was said and done with one another would be respected and kept secret unless the other told otherwise. That trust though, had obviously been broken.
Of course, over time, Riku had eventually warmed up to Kairi -- and even ended up liking her at one point.