People interrupt because they don't know better (children who have not yet learned how to take turns), because they are egotistic (they think that what they want to say is more important or interesting - they want the attention), as a domination power play (yes, that get's taught as a deliberate technique: LINK), because they are desperately impatient (they've have a thought and are sure they'll forget it unless they speak it immediately) or even because they believe they are being helpful (completing your sentence, making efficient use of time).

Another is if they're presently hyper-focused (like you're trying to be) and have accidentally let their filters lapse, thus effectively being like a little kid or an egotist.