Ever watch two people having a conversation, and neither of them are talking about the same thing?

A while back, I was having a conversation with a friend about politics. It started off pretty even keeled, but the longer we talked the more heated it became. I would make a point. My friend would make a point. Then I would make another point. Then so would my friend. And so that cycle of point-counterpoint continued, each of us building up our points as if there were an imaginary judge that would declare a winner.