Umm.. I guess, you don't have to indifferent to the person but to the trivial fights that often invade many relationships. And more than indifference, I guess observation is a better strategy to adopt in relationships.
For instance, when you have a fight with your girlfriend, instead of giving in to your emotions and saying or doing something you'd regret later, you could try to create a psychological distance within yourself and observe your own emotions as a spectator instead of letting them overpower you. I know that that's much easier said than done, but it would definitely enable you to act more mindfully!