I believe when people say that they are offended it is using a psychological trap to shut down the conversation about it.
By saying they are offended, they are trying to make their views superior to yours - end of conversation - no discussion. You don't get to talk anymore because I am offended so YOU are wrong.
It happens very often. It is a logical fallacy - appeal to emotion (or less common phrase - appeal to righteous indignation)
Type of red herring :-)