Why you let it pass
In that moment you calculate fast: how important was my point, how awkward will it be if I insist, how will I come across. The calculation almost always goes against you.
What you do not factor in: the others in the room noticed too, and they read your silence as agreement.
Why the usual advice does not land
Speak louder. Just keep going. Show presence. These are instructions that presuppose a different person from the one you are right now.
What you need is not more assertiveness, but a sentence small enough that you can say it even when your heart is pounding.
The sentence
I was not finished.
Four words, no accusation, no explanation. It attacks nobody, it only restores what was true anyway. That is exactly why it is hard to push back against.
What happens next
In the vast majority of cases: nothing. The other person stops talking, you continue, the conversation carries on normally.
That experience is the point. Not the insight that you would be allowed to, but the experience that it costs nothing.
If it does get awkward
Then it was awkward, and you got through it. That is information too, and more solid than the fear beforehand.