Classical v Romantic knowledge

I'm trying to break the habit of searching for information that proves what I believe, and instead change my beliefs to fit the known facts. Where the facts are not known, I wish to learn to keep an open mind. I witness regularly people presenting only what supports their belief, even when it's not true; they ignore any assertion that runs counter to their preformed belief. I'm not sure if it's a fallacy, or poor critical thinking skills, or what, but it is sadly pervasive.

But I know that intuition is also powerful, and that 'facts' can be misleading. In his book Blink, the power of thinking without thinking, Malcom Gladwell describes how decisions reached with 2 seconds of thinking can be more accurate than researched decisions. Gladwell states that he dislikes the term intuition because it is associated with emotion, and he wants to emphasize that 'rapid cognition' is intellectually based. I still prefer the term intuition because I believe that it is the balanced intertwining of intellect and emotion that allows for accurate rapid choice.

So I'm seeking to develop both research based belief and rapid cognition based belief. The former is what school can teach. The latter comes from experience, and I certainly don't know how to teach it. It's basically the same ideas that Pirsig puts forth in Zen and the Art of Motorcyle Maintenance with classical and romantic knowledge.