I wonder what would happen if you put her in some kind of activity that she sucked at and then, through hard work, she could improve. Like music lessons. Or maybe something with a social component–like sports or dance–where she could experience being the low girl on the totem pole.
Perhaps a little know-it-allness comes with being the eldest child? As a kid, I received wisdom from my older siblings, who let it be known that I was just a little baby who didn’t know nuttin’. I didn’t have to worry about maintaining high expectations because the older kids had done an effective job of lowering the bar! So maybe you can find some way to mitigate any undue sense of maturity by putting her in social situations where she is the youngest. Does she have older cousins she could hang out with?
My oldest daughter had some of those same traits and habits.
It turns out the most helpful thing we said to her was that people who don’t make mistakes are likely not doing anything of importance (I know this because she’s told me). She’s 25 now and reasonably socially successful–she has friends and can get along with most people, though she still is impatient with slower thinkers and those who do not express thoughts clearly.
We also went out of our way to teach her manners (as in listening, not interrupting, a modicum of tact) and how to show respect for the ideas and accomplishments of others. These things required lots of role-playing and reminders because it was not her natural inclination.
I do think some of this has to do with being the oldest, as well as a personality thing. Her next younger sibling is every bit as bright (perhaps brighter) but has a completely different nature.
Crap. I’m 27 and a graduate student and I still totally do the last. My parents are both lawyers and I’m not sure it ever occurred to them to instill in me that being smart =/= being right. Now I am in a wonderful relationship now where we don’t punish each other for admitting that we were wrong, thanks mostly to a gargantuan effort on the part of my partner to help me learn to communicate, not win. But I still have a hard time arguing with my parents, where no weakness must be shown and no quarter must be given.
I guess what I’m trying to say is, Toxylon, whatever you do, you’re doing right by your kiddo just by being aware of this. As she gets older, in addition to modeling humility with your spouse as johnpost suggests, I think it will help a lot for you to model this behavior when you argue with her, too (although I recognize that this may be a difficult balance at an age where you are, in fact, in charge of her and most always right). Give her practice in having a relationship where she can be wrong (i.e. vulnerable) and be safe.