Check out this YouTube video titled: How to stop people from talking over you.
The YouTube channel Charisma on Command have a bunch of great videos on EQ.
And after the two of you have talked over each other for a few seconds, they'll stop and say something like, "I'm sorry, what were you saying?" You may think it's an invitation to explain what you were trying to say. It isn't.
And if you're like me, at this point of what I laughingly call my career, your best move is to shrug and walk off.
It sounds like you were forced into a fight with a manager over whether your opinions, ideas and thoughts were worth hearing - to him.
Although he had an official position, he was not acting with decent authority: so his judgement of your ideas has no force or truth, but is just his.
Your ideas, opinions and thoughts themselves were never at stake. They existed before that manager, and they existed after. They exist now.
I think I still lean towards talking to a manager as a more effective strategy, and a culture where management lets this kind of thing happen isn't really one I want to be a part of anyway.
I’m not sure going to a manager will work. That’s like saying: Rather than adapting my behaviour, I’d rather go to someone in the group who has power and ask them to defend me...I would rather improve my social skills and navigate the company myself. This would build my EQ and make promotions more likely.
You can escalate and re-assert that your point is valid, but that's just escalation that can go both ways, it can result in your message being heard and it can also result in you being physically removed from the discussion; so if you choose to escalate, then you need to be certain about who'll "win" the escalation. If it's an internal team meeting and the 'interrupter' is your peer, then it's one context; if it's a customer-vendor meeting and the 'interrupter' is your boss, then that's a quite different context, and you'd better stop making that point as soon as you get a hint that it's not where he wants to direct the conversation (with the other party); your point may be valid but if making it here and now would harm the company negotiating position, then he gets to decide that your message shouldn't be told here and now.
A big aspect that's important is who's setting the topic of the discussion, and the limits of what's off-topic, disctracting or irrelevant? In an informal small discussion between peers usually that's everyone and includes you, but there are many cases where it's someone else. And in many cases that someone else should be interrupting people and ensuring that some things don't get listened to - moderating discussions is a valid need that's hard to do and often gets done less than it should, resulting in excessive ineffective long offtopic meetings.
I'd argue that much better way is to back off for a moment and try more diplomatic solution.