The reason for apparent anomalies is that "holistic" thinking can involve two different styles: pre-attentive thinking and far-mode thinking. That is, you can have cognition that could be described as holistic either by being unreflective (System 1) or by engaging in far-mode forms of reflection (System 2 offloads to System 1.) In Ulric Neisser's terms, what is being called "intuitive" might reflect distinctly deeper or distinctly shallower processing than what is called analytic. I sort this out in The deeper solution to the mystery of moralism.

You needn't buy my conclusions about morality to accept the analysis of modes as related to systems 1 and 2.