I read the headline and thought this was going to be about interrupting someone during conversation.
Some people have a tendency to not so much converse as to pontificate. If you are seeking input from someone, you have to give them the chance to give that input.
If you have an issue with a point someone made within their first two sentences, the rest of the speech doesn't matter, so it's almost rude to wait until they finish to tell them their original assumption was wrong. Or they go off on such a tangent that you both forget the original purpose of the conversation.
Hypothetically, if someone is complaining that their back is sore from all the glass bottles they carry around to hammer nails with, waiting for them to get into the fine minutiae about the embroidery on their glass bottle bag is just wasted time. You need to ask the immediate question, "Why are you using glass bottles to hammer nails?"
...sorry, should have let you finish. You were saying the same thing.
Those who expect an interruption once understanding has been reached, and those who expect complete statements before interruption.
The failure modes from when these two different approaches mix is either "awkward" or "rude".
Generally, if someone is rambling, interrupt them. (With exceptions like if someone is emotionally venting, let them release it).