✔ 最佳答案
anger or hurt are both possible responses to being offended. The person is telling you that they will be saying something that you could become offended by. It could make you angry, it could hurt your feelings, or whatever; you probably will not like what they say.
Often, "don't take offense" means that you are about to be insulted somehow. Sometimes the people actually believe they are doing you a favor, being helpful by telling you what is wrong with you. Often, they are just telling you something insulting because they want to, and just shove that "don't take offense" up front to be polite just before they are really rude.