A lot of people gave advice about opening up the relationship, but, to me, there doesn't seem to be any real desire from Marbit to open his relationship up (aside from the standard "it'd be nice to have sex with others" that almost every guy thinks
), he just doesn't want to catch shit for checking out another woman or having sexual thoughts about anyone but his girlfriend and who can blame him?
The fact is this woman is trying to dominate your mind, and make you feel guilty for retaining sexual thoughts. It's a mild form of emotional blackmail - "if you loved me, you wouldn't want to look at anyone else" and it holds no basis in reality.
If it was me, I'd basically say that I can't stop myself looking and I can't stop my brain responding but that if I've made a commitment to her then I will honour that, and that every time she gives you shit for your natural, human reaction to a beautiful woman, then she's just going to end up pushing you away.
But you've probably made the situation worse on yourself by promising to "try to change." If there's one thing I've learnt, promising something like that when you know full well that it's IMPOSSIBLE to change is a recipe for drama and disaster.
Just a quick caveat though, obviously you can't help finding people attractive, but there are rules of subtlety as well! If you're out in public with your girlfriend, then obviously try your hardest to be respectful to her - don't obviously check out girls, don't gawk and stare etc.