These are your personal preferences, not some "social contract". I'm completely fine with people interrupting me to correct something I said or to add an important detail I missed, and I tend to do the same.
To see slightly diverging behaviors as uncivilized, to unilaterally demand that people change it to suit your preferences, and especially to threaten people with physical violence seems really deeply troubling to me. I don't think that's a good attitude to have at all.
People have different cultural and personal expectations, quirks, even medical conditions (e.g. ADHD) that affect how they handle communication. You can ask people - politely - to try their best not to interrupt you because it makes communication difficult for you, otherwise walk away.
I also have ADHD which makes me more prone to interrupting people and while I try my best not to, it happens. If I'm troubleshooting a problem for you and by the end of your second sentence I know what the immediate next step is but you keep talking about some irrelevant back-story, I will probably interrupt you - either that or my brain will completely miss what you're saying for the next 5 minutes, making sure that the thought in my head doesn't just - poof, disappear.
Yes some people think I'm rude for that. No, I don't really care because it's not something I can change. Rude are the people unilaterally imposing arbitrary personal preferences onto other people.
You have the right idea what should take priority when trying to accomplish something.
If you interrupt me to correct me I actually admire it. Extra points if you get to do it twice in a sentence.
I'm taking about repeatedly interrupting the next step with irrelevant back story or worse, a not even related topic.
The big question I suppose is if your thoughts continue to go poof if you try harder to hold onto them.
This has never happened in your life. There is a one hundred percent chance that if somebody repeatedly interrupts you, you nod and picture what Sephiroth would do to them.
I ran into someone I didn't see for many many years. He told me that over time he realized I was the only one he ever had a real conversation with. Real was probably not the right word I think but everyone he knows including him takes great care to never let anyone finish a sentence. Everyone reminded him of me. He talked for 40 minutes straight, it was the most memorable life story full of unlikely favorable events. He really needed to get it off his chest too.
It was a memorable event for you that somebody said that they enjoyed talking to you?
His life took a few hilarious unexpected turns that worked out really well for him.