The number one problem is insecurity. That's why you focus on the fights the next day and that's why they get so bad. Deep down you are afraid you may not be right, so when you feel you are right and your girlfriend disagrees you feel you must force her to take your opinion to validate it.
I think the solution is a blend of self-confidence and proper perspective. At least the latter if you can't achieve the former. Your girlfriend sounds like a pretty great person in that she's willing to move past these fights and stick with you. You need to remember that the little thing you are arguing about is NOT so important, and that it does NOT reflect on your worth as a person whether or not your girlfriend agrees with you.
Try making this a regular tactic: "I value your opinion, but I just disagree this time." Let it go. Say that to her. You don't have to agree on everything.
Maybe once in a while listen to her and really consider her position, and you may find yourself even agreeing with her sometimes.
Since time began
the dead alone know peace.
Life is but melting snow.
--Nandai