To have a productive discussion, you need a method of discussing. What is step 1 in a discussion? What is step 2? What is step 3?
If you don't know, or don't have it in writing, why would you think you're ready for an intellectual discussion? That means you will follow a unknown or unclear method. In that case, if the method has any flaws, then you will have a hard time in the discussion (due to using a flawed method) and have a hard time understanding why the discussion isn't working well.
If your discussion method hasn't been analyzed with conscious, critical thinking, you should expect it to have lots of flaws. And if it isn't specified in writing, you should expect to change it mid-discussion according to your biases.
Reposting this from Basecamp. I think I've written this method up before somewhere but didn't find it.
A fair discussion methodology I've used before is to write two things at a time: one where you control discussion flow and one where the other person does. (E.g. you ask one question and answer one question. Or you make one argument and respond to one argument. It's one thing of your choice and one of the other guy's choice.) If a person says multiple things at once in their part, the recourse is to answer only one thing. They can then repeat one that was not answered yet. Control in your half is absolute and you can drop any topic and jump to anything else at any time – if someone wants an answer to something you drop, they can bring it up in their half.
A different way to view this method is: have two parallel conversations and synchronize their speed (they each get one step simultaneously).