I would suggest that if you primarily think in a fast, intuitive manner, then INTP doesn't match you because that antithetical to what INTP means. Perhaps you are reading too much into the "type descriptions" which tend to be stereotypically and not particular accurate (or are being too trusting of questionaire test results). Many of the types are similar to each other, so it's common to see oneself to an extent in more than one description.
To be an INTP means that your dominant thinking process is "Introverted Thinking" which is slow, reasoned, logical thinking that places a high emphasis on internal consistency. And that this is backed up with a secondary thinking process of "Extraverted Intuition" which is fast, intuitive thinking, which an emphasis on ideas and creative, divergent thought patterns. Or at least, that this was true of you as a young person.