Just like world_eater said, it's a phrase that denies one's own part in causing the offense. "I'm sorry you were offended" is like saying "I'm sorry it rained on you". A show of sympathy, perhaps, if not sarcastic, but not taking responsibility for any wrongdoing. "I'm sorry I caused you offense" or "I'm sorry I hurt your feelings" is slightly better, though still subtly foisting focus onto the person offended.
Best apology, to me, is "I'm sorry I screwed up/behaved offensively/[insert specific act], it won't happen again". Acknowledges both the act and one's responsibility for it, without having to bow and scrape and renounce one's dignity. Variations on that combined with changed behavior in that space, or an attempt to mend or better understand whatever caused offense if possible, usually gets a positive response, in my experience. I have seen one or two people who keep being nasty despite that, but they can be safely ignored.
Online SJ types tend to be highly focused on the power and complexity of words. Unfortunately, no one online can read your mind or see your face, so the effort to use careful wording takes place of tone as a way of showing sincerity.
no subject
Best apology, to me, is "I'm sorry I screwed up/behaved offensively/[insert specific act], it won't happen again". Acknowledges both the act and one's responsibility for it, without having to bow and scrape and renounce one's dignity. Variations on that combined with changed behavior in that space, or an attempt to mend or better understand whatever caused offense if possible, usually gets a positive response, in my experience. I have seen one or two people who keep being nasty despite that, but they can be safely ignored.
Online SJ types tend to be highly focused on the power and complexity of words. Unfortunately, no one online can read your mind or see your face, so the effort to use careful wording takes place of tone as a way of showing sincerity.