jms, my issue/concern with what you described in your first post is this.

It doesn't matter whether or not your position is "more logical" - you can disagree completely with someone else's point of view but complete a conversation while still communicating that you respect and enjoy their opinion. You simply aren't taking the time to do that.. or your boyfriend wouldn't have the responses you describe. "Success" in this art isn't determined by your logic, but rather by your boyfriend's response.

For example, instead of snapping to whatever the next logical step is, you could begin by saying "Yes, I see what you're saying, and that's a good thought - but here is my reply" or "I hadn't considered that idea.. could you explain how it addresses this point, though"

It's not the logic that's the problem - it's never the train of thought that is the problem. It's your additional desires to control the conversation (and by extension him) and the desire to always be right (and never admit anyone else could possibly actually have a point.. you spin around to make sure nobody actually has a chance to complete that task of "convincing" you of anything) that cause issues.

You don't need to work on your logic - you need to work on your empathy. He probably doesn't want to debate you on anything any more because he knows you take pleasure in running him down.