Interrupt someone and you’ll win the moment. Let them finish and you’ll win their respect.

Cutting in gets you the floor and costs you something you will not notice until later. People remember being talked over far longer than they remember your point, and they adjust how much they tell you next time. Letting someone finish is not politeness, it is the cheapest way to be trusted.

Try one full week of waiting two seconds after someone stops talking before you start. You will hear the part they were building up to, which is usually the part that mattered. People will also start saying more around you without knowing why.