There are two main reasons I know of why people interrupt.

1. They already know or think they know what the other person is going to say
2. They have an objection to what the other person is saying at the current moment of time, but they afraid they will forget that objection and the rebuttal argument by the time when it will be their turn to speak. Incidentally, this is the main reason why people seemingly respond to your question or narrative, but in reality what they say is just a continuation of what they were saying previously. In another word, if you don’t let them voice their objection right away, they lose the thread of what you are saying and just continue pretending that they are listening.