One of the great things about playing an instrument is that there are so many different strengths one can bring to the table. Some students are great with pattern recognition, spatial visualization, and music theory; some have a natural musicality in their physical technique; some have a great tonal memory and musical ear; and some have a tenacity and that allows them to make up for any deficits in other areas with sheer dedication and a great attitude.
I have never, ever, worked with a student who "just didn't have it" - everyone who puts in a bit of effort improves. Part of what allows everyone to have success with music is that playing music uses both the "intuitive" right brain and the "logical" left brain. Part of my job as a teacher is to observe which hemisphere appears to be dominant in a student and adjust my methods accordingly.
While I believe in building on strengths, there is often a need to compensate for a weakness in a particular area in order to improve overall musicianship. Right-brain, intuitive thinkers tend to see the whole and rather than the part. This means that they on an attempt to play a new song they will "feel" their way through it, looking for larger patterns rather than getting stuck on small details. While this relaxed ease is the eventual goal, the challenge is then to learn how to break things down and read (i.e., decode) individual notes when necessary. On the other hand, a left-brain, logical thinker will focus on decoding the notes individually and incorporating every detail. While this is important, this student will need to learn how to begin to let go and listen to where the music is going, without needing to control every note with a conscious thought.
Try this informal test to see which is your dominant hemisphere. For my part, I am evenly split between right and left brain dominance, which I think is what has helped me to work with and relate to a wide range of learning styles. I'm a strange bird: equal parts artist and administrator.