It's so strange to hear fighting on the train or the bus now that my girlfriend and I have more or less stopped arguing for the last year or so. Sure, there are moments here and there, but fighting no longer resonates with me as something I'm interested in taking a part in. When I hear other people battling back and forth, attempting to gain some kind of ground in the relationship, it sounds so odd, because I've realized that nobody ever wins in those kind of fights. There's really no point and you're only taking away from the relationship by "trying to win." A relationship needs to be like a really long "yes and" heavy improv scene. There can be conflict, but you can't disagree with who a person is and what that person represents. If you do, you end up with a crappy scene, much like the scenes I've witnessed recently on public transportation. It makes people uncomfortable and it only serves to make you feel good about yourself for about a second.
How do you learn to stop fighting? I suggest reading 7 Habits of Highly Effective People by Stephen Covey. It's a book with many great points about relationships, parenting and business partnerships and from this one book alone I was able to reform multiple aspects of my existence. Diffusing fighting in your life has to do with employing empathic listening, active love, win-win situations and a desire to use your time to fulfill your life goals. Unless one of your life goals is to act like a jerk, most of the time fighting won't get you closer to the person you want to be remembered as. I thoroughly recommend you check it out.
Here in consistent writing town, I worked on some character writing prompts on mentally and physically disabled people and I wrote a blog post on rainy day writing for those who have to get writing done despite the crappy weather outside :).