As you may have guessed by now, I think the answer is status. Specifically, to give offense is to imply that a person or group has or should have low status. Taking offense then becomes easy to explain: it’s to defend someone’s status from such an implication, out of a sense of either fairness or self-interest.
Why would anyone expect that?
What does it mean to be offended? How is it different from being insulted? Is an insult that is true not an insult?
Relevant: The Nature of Offense.
Seems to match this case perfectly.