My daughter did the very same thing when she was younger and still does on occasion. It was/is very frustrating but I think it is a result of her being both very intelligent and very strong-willed. She argues about things, even though we both know that she is "wrong". After a while of not really knowing how to deal with it, I decided to just ignore it. I realized that I don't always have to have the last say. When she talks back to me in this way, I just totally drop the subject altogether. It's been working pretty well because the number of times she does this has decreased dramatically. I think that she was just frustrated about being corrected all the time. I keep reminding myself that her tenacity will really pay off for her when she is older!