Stop fighting... I'll say if he doesn't want to lose in an argument then let him win if you really love him... As my friend said "it's better to lose in an argument than to lose you" hope this helps a little :)
Maybe you are spending to much time together? I don't know what you two have been fighting about, but try to figure out if the reason you are fighting is usually the same things, and try to change them.
I think at some point in a relationship , you get tired of each other and that's when your love counts the most - if you can't get along and compromise on somethings well both of you aren't ready for a steady relationship.