Your 6-year-old now
On one hand, your child understands that being fair means sharing and not leaving out other children, and that misbehavior brings appropriate consequences. On the other hand, sixes' obsession with rule-making and rule-breaking muddies the water. It can be hard to distinguish what's equitable when you can't agree on the rules. Just witness a group of 6-year-olds who spend more time creating the rules to a game than playing it.
Your child may also not understand that rules are adapted according to age or ability. They think everyone should follow the same rules, and their black-and-white mentality doesn't allow for what they see as parental "hypocrisy." "You get to stay up late. Why can't I?"
While you don't need to justify all your house rules, be open to discussing the ones that really frustrate your child. Ask her why she thinks they're unfair. Listen and validate. "I understand your frustration. It may seem unfair that you have to empty the dishwasher all the time. But your little brother isn't old enough to handle the knives. I ask him to pick up toys instead."