To quote Robert Heinlein, "Man is not a rational animal, he is a rationalising animal."
You start with the answer that boils down to your gut feeling (e.g. "cycle helmets are good and therefore should be used") and you selectively ignore, re-arrange, cherry-pick etc. evidence and arguments to support the predetermined conclusion. Since you're sure you're right the conclusion is the fundamental point and the arguments amount to reassurance rather than the way to get there.
We all do this to some extent, some are better than others at catching themselves.
There was a fascinating Horizon on BBC4 yesterday evening about this (How we make decisions) that distinguished the two decision making mechanisms humans use. They suggested (or the research they were reporting/presenting suggested) that such shortcomings to our decision making process cannot really be "trained out" as they are very deeply set in our nature. They showed some research involving trained (US government) security analysts and amateurs who had to identify a terrorist threat based on provided information and they all (except one amateur?) decided early who they considered the terrorist was and then used confirmation bias to "get the wrong answer".