If it's a really bad argument, I find going back to common ground helpful. Shared goals, shared values, etc. Then see where we veered in different directions.
I also find it very helpful for myself to take a looooong pause before answering if he's expressed his feelings in a way that makes me feel like he's trying to tell me I'm wrong, even though I feel right. It usually makes me feel defensive and reactive so I need to calm my brain down so that I can start to think rationally again (literally when you are feeling angry or hurt your brain goes into fight or flight mode and you process things differently.) Often the right/wrongness doesn't matter and there is a deeper misunderstanding happening.