I think "how to think" can be taught at least a little bit. In mathematics you learn a very formalized method of finding (usually) the single correct answer. In the humanities, with textual analysis, you learn a different type. But it does take practice, and adequate instructors. And of course the average person will never come to it quite as well as someone with the natural aptitude. I occasionally teach a course in informal logic, which is a sort of cross section between rhetoric and logic as applied to both argument construction, deconstruction, & analysis. I definitely see students progress along the way, starting with clumsy stumbling and proceeding to address new novel problems with decent aptitude.