It's not zero sum. You can both win, or both lose. Or she can win and you can lose, but only if she's not a very nice person (e.g. a controlling bitch). Or you can win and she can lose, but only if you're a controlling prick.
You win if you can resolve the issue and make her feel better without making major loss to yourself or the relationship. Usually, this involves her winning, as well.
You win if you can resolve the issue and make her feel better without making major loss to yourself or the relationship. Usually, this involves her winning, as well.