I prefer "being an arsehole". Rather person A saying something that "caused offence", person A acted like an arsehole.
I incidentally disagree with you completely. The blame is rightly on the victim. What offends is usually personal, vague and often illogical. It's not reasonable to hold anyone responsible for doing perceived offensive things (provided they don't actually do anything otherwise illegal; I shouldn't have to point this out but I'll hedge).
"It takes two to fight" means that if anyone tried to fight you, you had to go to a teacher and report them. That was the only sanctioned remedy.
It worked about as well as you'd imagine. I wonder what would happen if we applied the same logic to adult arguments and crimes.