For example, I say “There is no need to be rude” and the other person says “That’s ironic” just to shift the blame back at me.
Can I say “That’s double ironic” here or would it be wrong? To me “double ironic” means something that is ironic but also true hence “true”. Correct me if I am wrong though. Thanks in advance.
I think that accepts what they said too much. But then without knowing the details, I would just say that people that insist on being rude and get huffy when called on it are probably not people worth spending time with.
The perfect response would be to educate your accuser. Irony is a literary technique. There’s no such thing as “double irony”. If he’s trying to imply that your dismissal of rudeness was itself rude, the word they are looking for is “hypocritical”.
“Like rain on your wedding day?”
Tell them that they should have said “That’s rich”. It’ll make more sense and of course then you can retort “I am rubber and you are glue”
“The chemists prefer the term ‘Ferric’”
Punch them in the throat. Instantly shuts up anybody. And possibly kills them. Which would pretty much shut them up forever. Works as a response to just about anything.
Don’tcha think?
Anytime that word is used I always fall back on William Shatner’s great line from the (undeservedly) much-maligned Airplane 2, “I guess irony can be pretty ironic sometimes…”
I agree with “doncha think?” as being the best response.
My other proposal would be something like, “Now that I’ve been put in my place, we can proceed with civility.”
You could say “I bet you can’t define ‘ironic’”.
Respond with: “No, ironic would be, ‘There is no need to be rude, asshole.’”
Or, punch them in the throat, a la DCnDC.
“You keep using that word. I do not think it means what you think it means.”
Bonus points if you can say it in a faux Spanish accent.
I REALLY need to steal that. Thanks…! 
“Your face is ironic”
Hit them with an iron.
“That’s what she said!”
Seinfeld provides us with two.
Them: “That’s ironic.”
You: “What’s ironic?”
Them: “That you’re the one chastising someone for being rude.”
You: “No, what does that mean, ‘ironic’?”
And of course, “The jerk store called and they’re all out of YOU!” or “Yeah, well I had sex with your wife!”
I guess they gave us three.
Third for the throat punch thing.
My first thought was “Fuck you.” But I could go with the punch in the throat thing…
