This phrase means someone spoke so briefly or with such lack of explanation that their reply or statement was considered rude For example if you asked someone to help you with something and they simply replied No!, Their reply could be described as brief to the point of rudeness

The idiom here is "to the point of". It means "to the extent of" or "so [X] that it was [Y]". "Brief to the point of rudeness" would mean: "So brief that it was rude."