Watching the INTJ and INTP discussion lists, people who are new to the theory often mistake their secondary function for their dominant function
. INTJs, for example, often think of themselves as primarily rational in the sense of being "systematic", and reasonably infer that "thinking", perhaps "introverted thinking", would be their dominant function. INTPs often think of themselves as primarily imaginative, outside-the-box thinkers, and reasonably infer that "intuition", perhaps "introverted intuition", would be their dominant function.
Could it be that they're describing their favored extraverted attitude
? Casual, anecdotal evidence suggests that extraverts also typically identify with their secondary function, though. For example, ENTPs and ESTPs think of themselves as analytical and having a good "hands-on" understanding of things. "Let me get my hands on it and I can figure it out. It's just a magical talent of mine."
More examples: ISTPs and ISFPs often think of themselves as primarily "cool" or "hip". ISFJs and INFJs tend to understand themselves mainly in terms of their personal loyalties to others.