If you are counting each time you or your spouse 'wins' an argument, does a household chore, or takes over child care, you are keeping score. Keeping score is destructive to a marriage. Competition beyond light-hearted play can be dangerous to a loving relationship. It sets you both up as opponents on opposite sides when you want to be partners on the same team.
It's hard in our 'gimme' culture to have generosity of spirit. When we live with too much stress we fight for every inch of control we can get. When is being assertive actually being a bully? When is picking your battles really passively wimping out?
Why does it need to be one or the other?
Couples find harmony when they can genuinely trust one another enough that each partner has the other's happiness foremost in their hearts. That means my partner is ready to do something that causes him discomfort because to do so is needed to make me happy. At the same time I don't want him to be uncomfortable so I will do everything I can to minimize the need for his discomfort. And vice versa. See how it works?
The road to this ideal is bumpy but well worth taking. Negotiation is always necessary in a good relationship because we aren't, Thank God, clones of each other. If both parties have the other's interest truly at heart you can reach a win-win settlement.