I flip this around whenever someone stops an argument dead in its tracks to tell me they've been offended. Whenever my sister or cousin tell me this, they think it's the end and they can drop out unscathed.
That was, of course, until I came up with an excellent comeback: "I find it offensive that you were offended by me. I chose my words very carefully so as not to offend you." It sounds ludicrous, but in reality, it's bulletproof. Maybe it's not, but it beats apologizing.