It’s called Cooperative overlapping.
It seems self-evident. Starting to speak before another has finished violates their right to the floor. In formal contexts such as political debates, it breaches the rules. In casual conversation, it is simply rude.
But it’s not so simple. As a linguist who studies the mechanics of conversation, I’ve observed and documented that beginning to talk while another is talking can be a way of showing enthusiastic engagement with what the speaker is saying. Far from silencing them, it can be encouragement to keep going.
Highlighting content from my September 2021 newsletter.