It seems to me that some folks highly value a self-image of not offending others — to the extent that when they are informed that they have offended someone, they respond as if a scandalous accusation has been made against their honor, for which they are entitled to demand satisfaction.

Being labelled offensive is to experience a reputation attack. Being offended at said attack is not different in nature to being offended at anything else. Whether the attacks in question are legitimate depends on the details and depends on the preferences of the people in the social group and allegiances among them.

Further, conveying that something is offensive (for example, by signalling that they feel comfortable declaring "I feel offended") also amounts to either claiming status or rights for a group or asserting control over the local social rules. It can be expected that this will sometimes be countered. And it should be (sometimes). Otherwise people are encouraged to be offended at all the time as a means of control. See also: children throwing tantrums. Adults too, for that matter.