Every time there is any petty arguments over small matter, I would keep quiet and leave the place to cool off, my hubby knows that I am angry although I don't fight back, he will try to break the ice later
Ask yourself: If this is a "deal breaker"? If it is get out! If it's not learn to live without. There only two ways to experience joy and peace of mind in relationships. We either get what we want or we learn to be happy with what we have. Ultimately everyone is looking for someone who will love and appreciate them for who they are. Surly not every topic is worth causing tension in a relationship. Most petty arguments are (ego) driven. It's a case of too much (You & Me) and not enough (Us & We). When two people are "in love" their mate's happiness is just as important as their own.
If the argument is petty, then is surely doesn't really matter, so it is not a case of backing down, it is just a case of a different view. So you just don't argue about something silly or petty, leave it or agree to disagree.