Under what circumstances would a professor be offended at students taping or recording his or her lecture?
I do not believe it had anything to do with the act of being recorded by itself. Most universities are beginning a process of recording lectures for later consumption by the students anyway.

Instead in this case it is likely because the professor was unaware they were being recorded. They may do or say something that they regret or which gets them into trouble. If however they knew beforehand that they were being recorded it would be unlikely that they would do that since they know the repercussions would be more severe. I think it was an instinctive reaction to protect themselves from others using the recording against them.