Here's a Time Management technique to help you switch to and focus on the task at hand.
When I've had a conversation with someone who relentlessly interrupts to talk about something else, argues every point as soon as it's stated, or derails the task onto some tangent, it echoes in my mind for much longer. It puts me into a sort of jerky rhythm where I'm expecting that any small thing I try will be immediately opposed. It becomes difficult to concentrate even hours or days or even weeks later, with this rhythm in my head.
The problem is not so much interruption, it's the knee-jerk opposition to everything that's said or tried.
Simple solution: stay away from people like that.
Could you just ask them to please not interrupt, if that's bothering you?
My experience with massively interrupty, argumentative people is that asking them to please listen and then respond has no effect. They might say yes, but they just continue interrupting. They probably don't even realize they're doing it.
Could you tell them that they're interrupting a lot, if they don't know?
My experience is that they don't hear it. I've told some of these people five and ten times, only to hear, months later, upon getting short with them and bringing it up again, "Wow, I never knew that I interrupted so much or that it bothered you." And then more interruption. This was even after doing an exercise to make every interruption obvious. The exercise was that only the person holding a magic marker could speak: even as he kept grabbing for the magic marker in the middle of another person's sentence, even when it was explicitly pointed out that this was an interruption, he still didn't see it.
Hypothesis: there's just a certain percentage of people who have no empathy for other people's need to concentrate attention, and no amount of discussion or negotiation will open their eyes to that.
Isn't this just a clash between introverted and extraverted personality types? Might extraverts not have this problem?
It probably is. This isn't a solution for everyone, nor is it a problem that everyone has. If you have this problem of getting into a bad rhythm after dealing with relentless interrupters/arguers, a simple solution is to just avoid them.
There may be high costs to that, though, like quitting your job. So it would still be nice to know some techniques for persuading interrupters/arguers to cool it.
An idea for dealing with interrupters/opposers is to find a way to meet whatever need they're fulfilling by interrupting, but in a way that is less disruptive. Presumably this is a need to be heard and to respond creatively, when inspiration comes.
A possible way to do that is to define a structure for the conversation, where there is a specific slot for counterproposals, arguments against what is proposed, and tangents. Hand out pencils and pads of paper to jot down counterarguments as they occur instead of blurting them out.
I've tried this on one massively interrupty person with some success--someone who interrupts frequently in a group setting, usually to quibble. However, it has taken about six months of relentless remindings to please stay on topic and to please keep silent when someone else is talking, for perhaps a 50% improvement.
Another idea to deal with interrupters, if they continue to interrupt even after you've brought up the problem and they've agreed to stay on the current task, is to just walk out of the conversation the second they interrupt. Don't say anything, just walk out. If they protest or ask what you're doing, say briefly that you really need to focus on _____, and you're finding that difficult to do with this level of interruption and immediate argument. No blaming, just relate your action to your need to concentrate.
Miss Manners might not approve, but if they clearly have no audience for their interrupting, this quick biofeedback might wake them up.
Ask them for a cup of coffee, it always works!