I had this discussion with a friend at work. He's always complaining that I cut him off when he's telling a work story. I do this for two reasons. First, because I want to show how smart I am by guessing the conclusion of the story, or providing advice before he's finished. This sometimes works.
The second is the stronger reason. Once I understand the gist of the story, I want certain details to better understand it. I find it's much more efficient to interrupt and solicit those details than wait for them to come out in the telling of the story.
One of the amazing parts about working in my corporations are meetings with executives. They walk into a meeting and take over the conversation. It's not that they dominate the conversation by talking more or louder as many people do who enjoy hearing themselves talk. It's more that they want to guide the conversation to the issues that they think are important.
The first time I was in such a meeting, I sat in amazement as the executive interrupted the detailed powerpoint presentation, and attacked the important issues, some of which the presenter was attempting to avoid. I hate meetings, especially meaningless meetings. But by guiding the conversation in this way, the executives turned a potentially useless meeting into an exciting and productive one. At the end of the discussion, we walked away with a detailed plan, and covered the pertinent issues.
After leaving that first meeting, I vowed to emulate their example: I walk into every meeting, and where possible, guide the conversation in a more productive (and sometimes combative) manner. It sometimes goes over very well. It very much depends on the audience.