In my experience, people who don’t agree with you shout. Or at least raise their voice to get their point across.
And the more that someone raises their voice, the more entrenched they become.
All they can hear is the the sound of their own words.
So, naturally, they’re unlikely to start agreeing with you.
And if you raise your voice in answer, there’s only one way that this will go.
Instead, try dropping your own volume. Keep the intonation and inflection the same, just pull back on the volume – especially if your antagonist is at the other end of the meeting table.
Experiment with talking more and more quietly, until they are forced to stop and say:
“Sorry, can you repeat that?”
Once they’ve done this, there’s a chink in their armour and you can get your voice through.
They’ve acknowledged not only your presence, but your words as well.
You’re in. Now make those words count.