We can all agree that the most fun part of arguing is using the time the other person is talking to formulate your searing rebuttal. But if you went into this thing hoping that you might get people who disagree with you to hear what you're saying, you're going to need to really try to listen to them, too, says Smith.
The first step here is to genuinely be interested in what they're saying; assume that understanding their position more deeply is worthwhile and might help them understand you in return. "Let them know you're paying attention and care about what they're saying," says Smith.
You can say things like, "I don't understand where you're coming from. Can you explain it to me?" And after you've heard their side — again, you need to actually listen for this to work — you can say, "I just learned X, Y, and Z from what you said, and I get what you're saying. Would you be willing to listen to me share my side, too?"
There are some more tips for being a pro listener here.