Sometimes it's really hard to keep calm, even though you know and they know, they're wrong. I'm not talking about the times where you think you're right, but you could very well not be. I'm specifically talking about the times where you are straight up correct, no matter how you slice it.
Step one : take a deep breath, they obviously cannot see past their own ignorance
Step two : refrain from exerting physical force
Step three : try to empathize to the point where you can see how they got to where they are (you don't have to agree)
Step four : keep breathing
Step five : chalk this one up as a loss
Step six : smile. Grin and bear it, kill them with kindness, take the high road. Insert cliche quote here.
Step seven : make note. I say this because not only will this be a great point of reference, but it will ultimately help you reflect for (unavoidable) future situations.
Now I'm not saying to create a blog, or a journal that you have to write in religiously, where you feel chained, but I encourage you to make note of this situation. Whether it be a post-it, the back of a receipt, a note on your phone, or an email to yourself. Write. Shit. Down.
Try to incorporate some feels (new school term for feelings) in there too, how you're feeling right then, the most unbiased view you can jot down. Definitely revisit the note after some time has passed too, you might see things a bit clearer.
I try to do this whenever something absurd happens, so I can figure out how to work on avoiding that situation with that person in the future.
Sweeping conflict under the rug, while easy, builds up. There's only so much that can fit under there! Pretending that if time wears on it'll just disappear, is naive. Shit festers, shit explodes. Address things head on, and while they'll probably be uncomfortable as hell in the beginning, your relationship with that person will thank you for it in the long run.
I digress.