Provoking a negative emotional reaction is pretty much what offensive means. What else would it mean to be offended? For example, I have a negative emotional reaction when strangers on the internet tell me I might want to "do some reflection" — it's presumptuous, condescending, and impertinent. Especially when what they mean is: "don't make me feel ashamed for sticking remote-controlled devices up my butt" — an odd thing to get on one's high horse about.