they respond as if a scandalous accusation has been made against their honor,
That's because in today's world having a reputation as being "offensive"/"insensitive" can have a very negative effect on one's life and livelihood.
Having a reputation as smelly and unwashed can have a very negative effect on one's life and livelihood, too — but if someone points out that you smell bad, you are better served to update on that (and take a shower) rather than responding as if it is a slur. I don't think we want a social world in which people respond to negative feedback with overwhelming retaliatory defensiveness.
From Julian Sanchez, a brilliant idea unlikely to be implemented: