If someone is being racist, sexist, etc, then say that and explain if the person does not understand, why exactly what they said is racist or sexist. But simply saying "I'm offended" is itself meaningless. Lots of people get offended by all kinds of things, but that does not mean we should stop talking about it. For example my sister is offended at any criticism of catholicism. She is allowed to feel offended, people are allowed to criticise catholicism. Not a reason to shut people up.